2. The ergodicity problem in economics¶

Q 2.3 Coding the problem¶

1) Generate a pandas dataframe that simulates N coin tosses for w gamblers with the np.random.rand function. Set N=100 coin tosses and w=100 gamblers and add the prefix ’prob ’ to the column name.

In [1]:
import pandas as pd
import numpy as np

n = 100
w = 100

df = pd.DataFrame()
for i in range(100):
    data = np.random.randint(0, 2, size=n)
    temp_df = pd.DataFrame(data, columns=[f'prob_{i}'])
    df = pd.concat([df, temp_df], axis=1)

df
Out[1]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... prob_90 prob_91 prob_92 prob_93 prob_94 prob_95 prob_96 prob_97 prob_98 prob_99
0 0 1 0 0 0 1 0 1 0 1 ... 0 0 0 1 1 1 1 1 1 1
1 1 1 0 0 1 1 0 1 1 1 ... 1 1 0 1 0 0 0 1 1 1
2 1 0 1 1 1 1 0 0 1 0 ... 1 1 0 0 1 0 0 1 0 0
3 1 1 1 0 1 1 1 1 1 1 ... 1 1 1 1 1 0 1 0 0 1
4 0 0 1 1 0 0 1 1 0 0 ... 1 1 1 0 0 0 1 1 1 1
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
95 0 0 1 0 1 0 1 1 0 0 ... 1 1 1 0 0 0 1 0 1 0
96 1 1 1 1 1 0 0 1 1 1 ... 0 0 1 0 0 0 0 0 1 1
97 1 0 1 1 1 0 0 0 0 0 ... 1 0 0 0 0 0 1 1 0 1
98 1 1 1 1 0 1 1 0 0 1 ... 1 0 0 0 1 1 1 1 1 1
99 0 1 1 0 0 0 0 1 1 0 ... 1 1 1 0 0 0 0 1 1 0

100 rows × 100 columns

2) Initialize an additional w columns [’balance ’ + str(x)] with the value 100 to capture the initial wealth of 100$, where: x in range(0, w).

In [2]:
for x in range(0, w):
    data = [w] * n
    temp_df = pd.DataFrame(data, columns=[f'balance {x}'])
    df = pd.concat([df, temp_df], axis=1)

df
Out[2]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... balance 90 balance 91 balance 92 balance 93 balance 94 balance 95 balance 96 balance 97 balance 98 balance 99
0 0 1 0 0 0 1 0 1 0 1 ... 100 100 100 100 100 100 100 100 100 100
1 1 1 0 0 1 1 0 1 1 1 ... 100 100 100 100 100 100 100 100 100 100
2 1 0 1 1 1 1 0 0 1 0 ... 100 100 100 100 100 100 100 100 100 100
3 1 1 1 0 1 1 1 1 1 1 ... 100 100 100 100 100 100 100 100 100 100
4 0 0 1 1 0 0 1 1 0 0 ... 100 100 100 100 100 100 100 100 100 100
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
95 0 0 1 0 1 0 1 1 0 0 ... 100 100 100 100 100 100 100 100 100 100
96 1 1 1 1 1 0 0 1 1 1 ... 100 100 100 100 100 100 100 100 100 100
97 1 0 1 1 1 0 0 0 0 0 ... 100 100 100 100 100 100 100 100 100 100
98 1 1 1 1 0 1 1 0 0 1 ... 100 100 100 100 100 100 100 100 100 100
99 0 1 1 0 0 0 0 1 1 0 ... 100 100 100 100 100 100 100 100 100 100

100 rows × 200 columns

3) Create a two-level for loop that iterates through rows 1 to N first and columns w to 2×w next implementing the calculation logic for every prob-balance pair:

Screenshot%202022-10-14%20at%2010.06.18%20PM.png

In [3]:
for i in range(1,n):
    for j in range(w, 2*w):
        prob_value = df.iloc[i-1,j-100]
        if prob_value == 1:
            df.iloc[i,j] = df.iloc[i-1,j] * 1.5
        else:
            df.iloc[i,j] = df.iloc[i-1,j] * 0.6

df
Out[3]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... balance 90 balance 91 balance 92 balance 93 balance 94 balance 95 balance 96 balance 97 balance 98 balance 99
0 0 1 0 0 0 1 0 1 0 1 ... 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000
1 1 1 0 0 1 1 0 1 1 1 ... 60.000000 60.000000 60.000000 150.000000 150.000000 150.000000 150.000000 150.000000 150.000000 150.000000
2 1 0 1 1 1 1 0 0 1 0 ... 90.000000 90.000000 36.000000 225.000000 90.000000 90.000000 90.000000 225.000000 225.000000 225.000000
3 1 1 1 0 1 1 1 1 1 1 ... 135.000000 135.000000 21.600000 135.000000 135.000000 54.000000 54.000000 337.500000 135.000000 135.000000
4 0 0 1 1 0 0 1 1 0 0 ... 202.500000 202.500000 32.400000 202.500000 202.500000 32.400000 81.000000 202.500000 81.000000 202.500000
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
95 0 0 1 0 1 0 1 1 0 0 ... 1618.114584 0.010859 647.245833 2.651119 2.651119 0.001737 647.245833 6.627797 258.898333 103.559333
96 1 1 1 1 1 0 0 1 1 1 ... 2427.171875 0.016288 970.868750 1.590671 1.590671 0.001042 970.868750 3.976678 388.347500 62.135600
97 1 0 1 1 1 0 0 0 0 0 ... 1456.303125 0.009773 1456.303125 0.954403 0.954403 0.000625 582.521250 2.386007 582.521250 93.203400
98 1 1 1 1 0 1 1 0 0 1 ... 2184.454688 0.005864 873.781875 0.572642 0.572642 0.000375 873.781875 3.579011 349.512750 139.805100
99 0 1 1 0 0 0 0 1 1 0 ... 3276.682032 0.003518 524.269125 0.343585 0.858963 0.000563 1310.672813 5.368516 524.269125 209.707650

100 rows × 200 columns

In [4]:
df.to_csv('df.csv')

4) Plot the time trajectories (in gamble iterations) of the wealth per gambler and calculate how many gamblers have more than their initial 100 dollars. What happens when you increase N to 1,000 (Figure 2 in the original paper, except the red and blue line)? How many gamblers with more than 100 dollars do you have at t=1,000?

In [5]:
count = 0

for i in range(100,200):
    if df.iloc[-1,i] > 100:
        count += 1

print(f'Number of gambler whose wealth is more than 100$ : {count}')
Number of gambler whose wealth is more than 100$ : 18
In [6]:
import matplotlib.pyplot as plt

for i in range(100,200):
    temp_df = df.iloc[:,[i]].copy()
    plt.plot(temp_df)
    plt.title(df.columns[i])
    plt.xlabel('Time in gamble rounds')
    plt.ylabel('Wealth')
    plt.show()
In [7]:
plt.figure(figsize=(12, 12))
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
display(plt.plot(df))
[<matplotlib.lines.Line2D at 0x15391c05760>,
 <matplotlib.lines.Line2D at 0x15391c057c0>,
 <matplotlib.lines.Line2D at 0x15391c058e0>,
 <matplotlib.lines.Line2D at 0x15391c05a00>,
 <matplotlib.lines.Line2D at 0x15391c05b20>,
 <matplotlib.lines.Line2D at 0x15391c05c40>,
 <matplotlib.lines.Line2D at 0x15391c05d60>,
 <matplotlib.lines.Line2D at 0x15391c05e80>,
 <matplotlib.lines.Line2D at 0x15391c05fa0>,
 <matplotlib.lines.Line2D at 0x15391c22100>,
 <matplotlib.lines.Line2D at 0x15391c05790>,
 <matplotlib.lines.Line2D at 0x15391c22220>,
 <matplotlib.lines.Line2D at 0x15391c22430>,
 <matplotlib.lines.Line2D at 0x15391c22550>,
 <matplotlib.lines.Line2D at 0x15391c22670>,
 <matplotlib.lines.Line2D at 0x15391c22790>,
 <matplotlib.lines.Line2D at 0x15391c228b0>,
 <matplotlib.lines.Line2D at 0x15391c229d0>,
 <matplotlib.lines.Line2D at 0x15391c22af0>,
 <matplotlib.lines.Line2D at 0x15391c22c10>,
 <matplotlib.lines.Line2D at 0x15391c22d30>,
 <matplotlib.lines.Line2D at 0x15391c22e50>,
 <matplotlib.lines.Line2D at 0x15391c22f70>,
 <matplotlib.lines.Line2D at 0x15391c330d0>,
 <matplotlib.lines.Line2D at 0x15391c331f0>,
 <matplotlib.lines.Line2D at 0x15391c33310>,
 <matplotlib.lines.Line2D at 0x15391c33430>,
 <matplotlib.lines.Line2D at 0x15391c33550>,
 <matplotlib.lines.Line2D at 0x15391c33670>,
 <matplotlib.lines.Line2D at 0x15391c33790>,
 <matplotlib.lines.Line2D at 0x15391c338b0>,
 <matplotlib.lines.Line2D at 0x15391c339d0>,
 <matplotlib.lines.Line2D at 0x15391c33af0>,
 <matplotlib.lines.Line2D at 0x15391c33c10>,
 <matplotlib.lines.Line2D at 0x15391c33d30>,
 <matplotlib.lines.Line2D at 0x15391c33e50>,
 <matplotlib.lines.Line2D at 0x15391c33f70>,
 <matplotlib.lines.Line2D at 0x15391c3f0d0>,
 <matplotlib.lines.Line2D at 0x15391c3f1f0>,
 <matplotlib.lines.Line2D at 0x15391c3f310>,
 <matplotlib.lines.Line2D at 0x15391c3f430>,
 <matplotlib.lines.Line2D at 0x15391c3f550>,
 <matplotlib.lines.Line2D at 0x15391c3f670>,
 <matplotlib.lines.Line2D at 0x15391c3f790>,
 <matplotlib.lines.Line2D at 0x15391c3f8b0>,
 <matplotlib.lines.Line2D at 0x15391c3f9d0>,
 <matplotlib.lines.Line2D at 0x15391c3faf0>,
 <matplotlib.lines.Line2D at 0x15391c3fc10>,
 <matplotlib.lines.Line2D at 0x15391c3fd30>,
 <matplotlib.lines.Line2D at 0x15391c3fe50>,
 <matplotlib.lines.Line2D at 0x15391c3ff70>,
 <matplotlib.lines.Line2D at 0x15391e390d0>,
 <matplotlib.lines.Line2D at 0x15391e391f0>,
 <matplotlib.lines.Line2D at 0x15391e39310>,
 <matplotlib.lines.Line2D at 0x15391e39430>,
 <matplotlib.lines.Line2D at 0x15391e39550>,
 <matplotlib.lines.Line2D at 0x15391e39670>,
 <matplotlib.lines.Line2D at 0x15391e39790>,
 <matplotlib.lines.Line2D at 0x15391e398b0>,
 <matplotlib.lines.Line2D at 0x15391e399d0>,
 <matplotlib.lines.Line2D at 0x15391e39af0>,
 <matplotlib.lines.Line2D at 0x15391e39c10>,
 <matplotlib.lines.Line2D at 0x15391e39d30>,
 <matplotlib.lines.Line2D at 0x15391e39e50>,
 <matplotlib.lines.Line2D at 0x15391e39f70>,
 <matplotlib.lines.Line2D at 0x15391e0e0d0>,
 <matplotlib.lines.Line2D at 0x15391e0e1f0>,
 <matplotlib.lines.Line2D at 0x15391e0e310>,
 <matplotlib.lines.Line2D at 0x15391e0e430>,
 <matplotlib.lines.Line2D at 0x15391e0e550>,
 <matplotlib.lines.Line2D at 0x15391e0e670>,
 <matplotlib.lines.Line2D at 0x15391e0e790>,
 <matplotlib.lines.Line2D at 0x15391e0e8b0>,
 <matplotlib.lines.Line2D at 0x15391e0e9d0>,
 <matplotlib.lines.Line2D at 0x15391e0eaf0>,
 <matplotlib.lines.Line2D at 0x15391e0ec10>,
 <matplotlib.lines.Line2D at 0x15391e0ed30>,
 <matplotlib.lines.Line2D at 0x15391e0ee50>,
 <matplotlib.lines.Line2D at 0x15391e0ef70>,
 <matplotlib.lines.Line2D at 0x15391e170d0>,
 <matplotlib.lines.Line2D at 0x15391e171f0>,
 <matplotlib.lines.Line2D at 0x15391e17310>,
 <matplotlib.lines.Line2D at 0x15391e17430>,
 <matplotlib.lines.Line2D at 0x15391e17550>,
 <matplotlib.lines.Line2D at 0x15391e17670>,
 <matplotlib.lines.Line2D at 0x15391e17790>,
 <matplotlib.lines.Line2D at 0x15391e178b0>,
 <matplotlib.lines.Line2D at 0x15391e179d0>,
 <matplotlib.lines.Line2D at 0x15391e17af0>,
 <matplotlib.lines.Line2D at 0x15391e17c10>,
 <matplotlib.lines.Line2D at 0x15391e17d30>,
 <matplotlib.lines.Line2D at 0x15391e17e50>,
 <matplotlib.lines.Line2D at 0x15391e17f70>,
 <matplotlib.lines.Line2D at 0x15391e050d0>,
 <matplotlib.lines.Line2D at 0x15391e051f0>,
 <matplotlib.lines.Line2D at 0x15391e05310>,
 <matplotlib.lines.Line2D at 0x15391e05430>,
 <matplotlib.lines.Line2D at 0x15391e05550>,
 <matplotlib.lines.Line2D at 0x15391e05670>,
 <matplotlib.lines.Line2D at 0x15391e05790>,
 <matplotlib.lines.Line2D at 0x15391e058b0>,
 <matplotlib.lines.Line2D at 0x15391e059d0>,
 <matplotlib.lines.Line2D at 0x15391e05af0>,
 <matplotlib.lines.Line2D at 0x15391e05c10>,
 <matplotlib.lines.Line2D at 0x15391e05d30>,
 <matplotlib.lines.Line2D at 0x15391e05e50>,
 <matplotlib.lines.Line2D at 0x15391e05f70>,
 <matplotlib.lines.Line2D at 0x15391e1b0d0>,
 <matplotlib.lines.Line2D at 0x15391e1b1f0>,
 <matplotlib.lines.Line2D at 0x15391e1b310>,
 <matplotlib.lines.Line2D at 0x15391e1b430>,
 <matplotlib.lines.Line2D at 0x15391e1b550>,
 <matplotlib.lines.Line2D at 0x15391e1b670>,
 <matplotlib.lines.Line2D at 0x15391e1b790>,
 <matplotlib.lines.Line2D at 0x15391e1b8b0>,
 <matplotlib.lines.Line2D at 0x15391e1b9d0>,
 <matplotlib.lines.Line2D at 0x15391e1baf0>,
 <matplotlib.lines.Line2D at 0x15391e1bc10>,
 <matplotlib.lines.Line2D at 0x15391e1bd30>,
 <matplotlib.lines.Line2D at 0x15391e1be50>,
 <matplotlib.lines.Line2D at 0x15391e1bf70>,
 <matplotlib.lines.Line2D at 0x15391e310d0>,
 <matplotlib.lines.Line2D at 0x15391e311f0>,
 <matplotlib.lines.Line2D at 0x15391e31310>,
 <matplotlib.lines.Line2D at 0x15391e31430>,
 <matplotlib.lines.Line2D at 0x15391e31550>,
 <matplotlib.lines.Line2D at 0x15391e31670>,
 <matplotlib.lines.Line2D at 0x15391e31790>,
 <matplotlib.lines.Line2D at 0x15391e318b0>,
 <matplotlib.lines.Line2D at 0x15391e319d0>,
 <matplotlib.lines.Line2D at 0x15391e31af0>,
 <matplotlib.lines.Line2D at 0x15391e31c10>,
 <matplotlib.lines.Line2D at 0x15391e31d30>,
 <matplotlib.lines.Line2D at 0x15391e31e50>,
 <matplotlib.lines.Line2D at 0x15391e31f70>,
 <matplotlib.lines.Line2D at 0x15391e350d0>,
 <matplotlib.lines.Line2D at 0x15391e351f0>,
 <matplotlib.lines.Line2D at 0x15391e35310>,
 <matplotlib.lines.Line2D at 0x15391e35430>,
 <matplotlib.lines.Line2D at 0x15391e35550>,
 <matplotlib.lines.Line2D at 0x15391e35670>,
 <matplotlib.lines.Line2D at 0x15391e35790>,
 <matplotlib.lines.Line2D at 0x15391e358b0>,
 <matplotlib.lines.Line2D at 0x15391e359d0>,
 <matplotlib.lines.Line2D at 0x15391e35af0>,
 <matplotlib.lines.Line2D at 0x15391e35c10>,
 <matplotlib.lines.Line2D at 0x15391e35d30>,
 <matplotlib.lines.Line2D at 0x15391e35e50>,
 <matplotlib.lines.Line2D at 0x15391e35f70>,
 <matplotlib.lines.Line2D at 0x15391e3a0d0>,
 <matplotlib.lines.Line2D at 0x15391e3a1f0>,
 <matplotlib.lines.Line2D at 0x15391e3a310>,
 <matplotlib.lines.Line2D at 0x15391e3a430>,
 <matplotlib.lines.Line2D at 0x15391e3a550>,
 <matplotlib.lines.Line2D at 0x15391e3a670>,
 <matplotlib.lines.Line2D at 0x15391e3a790>,
 <matplotlib.lines.Line2D at 0x15391e3a8b0>,
 <matplotlib.lines.Line2D at 0x15391e3a9d0>,
 <matplotlib.lines.Line2D at 0x15391e3aaf0>,
 <matplotlib.lines.Line2D at 0x15391e3ac10>,
 <matplotlib.lines.Line2D at 0x15391e3ad30>,
 <matplotlib.lines.Line2D at 0x15391e3ae50>,
 <matplotlib.lines.Line2D at 0x15391e3af70>,
 <matplotlib.lines.Line2D at 0x15391e100d0>,
 <matplotlib.lines.Line2D at 0x15391e101f0>,
 <matplotlib.lines.Line2D at 0x15391e10310>,
 <matplotlib.lines.Line2D at 0x15391e10430>,
 <matplotlib.lines.Line2D at 0x15391e10550>,
 <matplotlib.lines.Line2D at 0x15391e10670>,
 <matplotlib.lines.Line2D at 0x15391e10790>,
 <matplotlib.lines.Line2D at 0x15391e108b0>,
 <matplotlib.lines.Line2D at 0x15391e109d0>,
 <matplotlib.lines.Line2D at 0x15391e10af0>,
 <matplotlib.lines.Line2D at 0x15391e10c10>,
 <matplotlib.lines.Line2D at 0x15391e10d30>,
 <matplotlib.lines.Line2D at 0x15391e10e50>,
 <matplotlib.lines.Line2D at 0x15391e10f70>,
 <matplotlib.lines.Line2D at 0x15391d0e0d0>,
 <matplotlib.lines.Line2D at 0x15391d0e1f0>,
 <matplotlib.lines.Line2D at 0x15391d0e310>,
 <matplotlib.lines.Line2D at 0x15391d0e430>,
 <matplotlib.lines.Line2D at 0x15391d0e550>,
 <matplotlib.lines.Line2D at 0x15391d0e670>,
 <matplotlib.lines.Line2D at 0x15391d0e790>,
 <matplotlib.lines.Line2D at 0x15391d0e8b0>,
 <matplotlib.lines.Line2D at 0x15391d0e9d0>,
 <matplotlib.lines.Line2D at 0x15391d0eaf0>,
 <matplotlib.lines.Line2D at 0x15391d0ec10>,
 <matplotlib.lines.Line2D at 0x15391d0ed30>,
 <matplotlib.lines.Line2D at 0x15391d0ee50>,
 <matplotlib.lines.Line2D at 0x15391d0ef70>,
 <matplotlib.lines.Line2D at 0x15391d090d0>,
 <matplotlib.lines.Line2D at 0x15391d091f0>,
 <matplotlib.lines.Line2D at 0x15391d09310>,
 <matplotlib.lines.Line2D at 0x15391d09430>,
 <matplotlib.lines.Line2D at 0x15391d09550>,
 <matplotlib.lines.Line2D at 0x15391d09670>,
 <matplotlib.lines.Line2D at 0x15391d09790>,
 <matplotlib.lines.Line2D at 0x15391d098b0>,
 <matplotlib.lines.Line2D at 0x15391d099d0>]

N = 1000¶

In [8]:
n = 1000
w = 100

df1 = pd.DataFrame()
for i in range(100):
    data = np.random.randint(0, 2, size=n)
    temp_df = pd.DataFrame(data, columns=[f'prob_{i}'])
    df1 = pd.concat([df1, temp_df], axis=1)

for x in range(0, w):
    data = [w] * n
    temp_df = pd.DataFrame(data, columns=[f'balance {x}'])
    df1 = pd.concat([df1, temp_df], axis=1)

for i in range(1,n):
    for j in range(w, 2*w):
        prob_value = df1.iloc[i-1,j-100]
        if prob_value == 1:
            df1.iloc[i,j] = df1.iloc[i-1,j] * 1.5
        else:
            df1.iloc[i,j] = df1.iloc[i-1,j] * 0.6

df1.to_csv('df1.csv')

count = 0

for i in range(100,200):
    if df1.iloc[-1,i] > 100:
        count += 1

print(f'Number of gambler whose wealth is more than 100$ : {count}')
Number of gambler whose wealth is more than 100$ : 0
In [9]:
for i in range(100,200):
    temp_df = df1.iloc[:,[i]].copy()
    plt.plot(temp_df)
    plt.title(df1.columns[i])
    plt.xlabel('Time in gamble rounds')
    plt.ylabel('Wealth')
    plt.show()
In [10]:
plt.figure(figsize=(24, 24))
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
display(plt.plot(df1))
[<matplotlib.lines.Line2D at 0x1538d0f1190>,
 <matplotlib.lines.Line2D at 0x1538edaa580>,
 <matplotlib.lines.Line2D at 0x153909a4bb0>,
 <matplotlib.lines.Line2D at 0x153909a49d0>,
 <matplotlib.lines.Line2D at 0x153909a4f40>,
 <matplotlib.lines.Line2D at 0x153909a4640>,
 <matplotlib.lines.Line2D at 0x1538d0ea370>,
 <matplotlib.lines.Line2D at 0x15391c57d60>,
 <matplotlib.lines.Line2D at 0x15391c57ca0>,
 <matplotlib.lines.Line2D at 0x15391c57a60>,
 <matplotlib.lines.Line2D at 0x1538d0e50d0>,
 <matplotlib.lines.Line2D at 0x15391c57700>,
 <matplotlib.lines.Line2D at 0x15391c576a0>,
 <matplotlib.lines.Line2D at 0x15391c57340>,
 <matplotlib.lines.Line2D at 0x15391c57460>,
 <matplotlib.lines.Line2D at 0x15391c57040>,
 <matplotlib.lines.Line2D at 0x15391c572e0>,
 <matplotlib.lines.Line2D at 0x15391c57d00>,
 <matplotlib.lines.Line2D at 0x15391a9a520>,
 <matplotlib.lines.Line2D at 0x15391a9a0d0>,
 <matplotlib.lines.Line2D at 0x15391a9abe0>,
 <matplotlib.lines.Line2D at 0x15391a9ad00>,
 <matplotlib.lines.Line2D at 0x15391a9aac0>,
 <matplotlib.lines.Line2D at 0x15391a9a9d0>,
 <matplotlib.lines.Line2D at 0x15391a9abb0>,
 <matplotlib.lines.Line2D at 0x15391a9ad60>,
 <matplotlib.lines.Line2D at 0x15391a9a0a0>,
 <matplotlib.lines.Line2D at 0x15391a9ad90>,
 <matplotlib.lines.Line2D at 0x15391a9a970>,
 <matplotlib.lines.Line2D at 0x15391a9a8b0>,
 <matplotlib.lines.Line2D at 0x15391a9a640>,
 <matplotlib.lines.Line2D at 0x15391a9af70>,
 <matplotlib.lines.Line2D at 0x15391d5cbb0>,
 <matplotlib.lines.Line2D at 0x15391d5c730>,
 <matplotlib.lines.Line2D at 0x15391d5c520>,
 <matplotlib.lines.Line2D at 0x15391d5c370>,
 <matplotlib.lines.Line2D at 0x15391d5c670>,
 <matplotlib.lines.Line2D at 0x15391d5c580>,
 <matplotlib.lines.Line2D at 0x15391d5cbe0>,
 <matplotlib.lines.Line2D at 0x15391d5c340>,
 <matplotlib.lines.Line2D at 0x15391d5ce80>,
 <matplotlib.lines.Line2D at 0x15391d5ca00>,
 <matplotlib.lines.Line2D at 0x15391d5c040>,
 <matplotlib.lines.Line2D at 0x15391d5c7c0>,
 <matplotlib.lines.Line2D at 0x15391d5c6d0>,
 <matplotlib.lines.Line2D at 0x15391d5c0a0>,
 <matplotlib.lines.Line2D at 0x1538f462820>,
 <matplotlib.lines.Line2D at 0x1538f462400>,
 <matplotlib.lines.Line2D at 0x15391a684c0>,
 <matplotlib.lines.Line2D at 0x15391a68e80>,
 <matplotlib.lines.Line2D at 0x15391a68a60>,
 <matplotlib.lines.Line2D at 0x15391a680d0>,
 <matplotlib.lines.Line2D at 0x15391a681f0>,
 <matplotlib.lines.Line2D at 0x15391a68d30>,
 <matplotlib.lines.Line2D at 0x15391a68df0>,
 <matplotlib.lines.Line2D at 0x15391a68760>,
 <matplotlib.lines.Line2D at 0x15391a68cd0>,
 <matplotlib.lines.Line2D at 0x15391a68af0>,
 <matplotlib.lines.Line2D at 0x15391a682e0>,
 <matplotlib.lines.Line2D at 0x15391a68e20>,
 <matplotlib.lines.Line2D at 0x15391a68d00>,
 <matplotlib.lines.Line2D at 0x15391a685b0>,
 <matplotlib.lines.Line2D at 0x15391e4bb80>,
 <matplotlib.lines.Line2D at 0x15391e4be50>,
 <matplotlib.lines.Line2D at 0x15391e4b6d0>,
 <matplotlib.lines.Line2D at 0x15391e4bbb0>,
 <matplotlib.lines.Line2D at 0x15391e4bd00>,
 <matplotlib.lines.Line2D at 0x15391e4b400>,
 <matplotlib.lines.Line2D at 0x15391e4b3d0>,
 <matplotlib.lines.Line2D at 0x15391e4b490>,
 <matplotlib.lines.Line2D at 0x15391e4bf40>,
 <matplotlib.lines.Line2D at 0x15391e4b430>,
 <matplotlib.lines.Line2D at 0x15391e4b7c0>,
 <matplotlib.lines.Line2D at 0x15391e4bb50>,
 <matplotlib.lines.Line2D at 0x15391e4b370>,
 <matplotlib.lines.Line2D at 0x15391e4b760>,
 <matplotlib.lines.Line2D at 0x15391ebf550>,
 <matplotlib.lines.Line2D at 0x15391ebff70>,
 <matplotlib.lines.Line2D at 0x15391ebf520>,
 <matplotlib.lines.Line2D at 0x15391ebf2e0>,
 <matplotlib.lines.Line2D at 0x15391ebf3a0>,
 <matplotlib.lines.Line2D at 0x15391ebf6a0>,
 <matplotlib.lines.Line2D at 0x15391ebf7c0>,
 <matplotlib.lines.Line2D at 0x15391ebf0d0>,
 <matplotlib.lines.Line2D at 0x15391ebfc10>,
 <matplotlib.lines.Line2D at 0x15391ebf280>,
 <matplotlib.lines.Line2D at 0x15391ebf220>,
 <matplotlib.lines.Line2D at 0x15391ebfb50>,
 <matplotlib.lines.Line2D at 0x15391ebfaf0>,
 <matplotlib.lines.Line2D at 0x15391ebf430>,
 <matplotlib.lines.Line2D at 0x15391daaf40>,
 <matplotlib.lines.Line2D at 0x15391daae50>,
 <matplotlib.lines.Line2D at 0x15391daaeb0>,
 <matplotlib.lines.Line2D at 0x15391daa580>,
 <matplotlib.lines.Line2D at 0x15391daa190>,
 <matplotlib.lines.Line2D at 0x15391daa9a0>,
 <matplotlib.lines.Line2D at 0x15391daa4f0>,
 <matplotlib.lines.Line2D at 0x15391daafd0>,
 <matplotlib.lines.Line2D at 0x15391daa280>,
 <matplotlib.lines.Line2D at 0x15391daac70>,
 <matplotlib.lines.Line2D at 0x15391daad30>,
 <matplotlib.lines.Line2D at 0x15391daa310>,
 <matplotlib.lines.Line2D at 0x15391daa880>,
 <matplotlib.lines.Line2D at 0x15391daab50>,
 <matplotlib.lines.Line2D at 0x153909bea30>,
 <matplotlib.lines.Line2D at 0x153909be070>,
 <matplotlib.lines.Line2D at 0x153909be3d0>,
 <matplotlib.lines.Line2D at 0x153909be700>,
 <matplotlib.lines.Line2D at 0x153909be880>,
 <matplotlib.lines.Line2D at 0x153909be310>,
 <matplotlib.lines.Line2D at 0x153909bef70>,
 <matplotlib.lines.Line2D at 0x153909be430>,
 <matplotlib.lines.Line2D at 0x153909beca0>,
 <matplotlib.lines.Line2D at 0x153909be1c0>,
 <matplotlib.lines.Line2D at 0x153909be6a0>,
 <matplotlib.lines.Line2D at 0x153909be130>,
 <matplotlib.lines.Line2D at 0x153909becd0>,
 <matplotlib.lines.Line2D at 0x15391a0ddc0>,
 <matplotlib.lines.Line2D at 0x15391a0dfa0>,
 <matplotlib.lines.Line2D at 0x15391a0de50>,
 <matplotlib.lines.Line2D at 0x15391a0d160>,
 <matplotlib.lines.Line2D at 0x15391a0db80>,
 <matplotlib.lines.Line2D at 0x15391a0d190>,
 <matplotlib.lines.Line2D at 0x15391a0d4c0>,
 <matplotlib.lines.Line2D at 0x15391a0da00>,
 <matplotlib.lines.Line2D at 0x15391a0d550>,
 <matplotlib.lines.Line2D at 0x15391a0d0a0>,
 <matplotlib.lines.Line2D at 0x15391a0d280>,
 <matplotlib.lines.Line2D at 0x15391a0d700>,
 <matplotlib.lines.Line2D at 0x15391a0d880>,
 <matplotlib.lines.Line2D at 0x15391a0dd90>,
 <matplotlib.lines.Line2D at 0x15391de8a90>,
 <matplotlib.lines.Line2D at 0x15391de8460>,
 <matplotlib.lines.Line2D at 0x15391de8af0>,
 <matplotlib.lines.Line2D at 0x15391de8580>,
 <matplotlib.lines.Line2D at 0x15391de8c40>,
 <matplotlib.lines.Line2D at 0x15391de8a00>,
 <matplotlib.lines.Line2D at 0x15391de8670>,
 <matplotlib.lines.Line2D at 0x15391de8dc0>,
 <matplotlib.lines.Line2D at 0x15391de8310>,
 <matplotlib.lines.Line2D at 0x15391de83a0>,
 <matplotlib.lines.Line2D at 0x15391de82b0>,
 <matplotlib.lines.Line2D at 0x15391de8f10>,
 <matplotlib.lines.Line2D at 0x15391de8ca0>,
 <matplotlib.lines.Line2D at 0x1538fb66100>,
 <matplotlib.lines.Line2D at 0x15390245910>,
 <matplotlib.lines.Line2D at 0x15391d92760>,
 <matplotlib.lines.Line2D at 0x15391d92940>,
 <matplotlib.lines.Line2D at 0x15391d92460>,
 <matplotlib.lines.Line2D at 0x15391d925e0>,
 <matplotlib.lines.Line2D at 0x15391d92ac0>,
 <matplotlib.lines.Line2D at 0x15391d92370>,
 <matplotlib.lines.Line2D at 0x15391d92670>,
 <matplotlib.lines.Line2D at 0x15391d92b20>,
 <matplotlib.lines.Line2D at 0x15391d923a0>,
 <matplotlib.lines.Line2D at 0x15391d92040>,
 <matplotlib.lines.Line2D at 0x15391d92c10>,
 <matplotlib.lines.Line2D at 0x15391d92e50>,
 <matplotlib.lines.Line2D at 0x15391d92580>,
 <matplotlib.lines.Line2D at 0x15391d928e0>,
 <matplotlib.lines.Line2D at 0x15391d28d60>,
 <matplotlib.lines.Line2D at 0x15391d28250>,
 <matplotlib.lines.Line2D at 0x15391d284c0>,
 <matplotlib.lines.Line2D at 0x15391d28df0>,
 <matplotlib.lines.Line2D at 0x15391d28880>,
 <matplotlib.lines.Line2D at 0x15391d28820>,
 <matplotlib.lines.Line2D at 0x15391d28130>,
 <matplotlib.lines.Line2D at 0x15391d28ac0>,
 <matplotlib.lines.Line2D at 0x15391d286d0>,
 <matplotlib.lines.Line2D at 0x15391d28730>,
 <matplotlib.lines.Line2D at 0x15391d282e0>,
 <matplotlib.lines.Line2D at 0x15391d289d0>,
 <matplotlib.lines.Line2D at 0x15391d28a60>,
 <matplotlib.lines.Line2D at 0x15391d28670>,
 <matplotlib.lines.Line2D at 0x15391cd6cd0>,
 <matplotlib.lines.Line2D at 0x15391cd6f40>,
 <matplotlib.lines.Line2D at 0x15391cd6d30>,
 <matplotlib.lines.Line2D at 0x15391cd6460>,
 <matplotlib.lines.Line2D at 0x15391cd6dc0>,
 <matplotlib.lines.Line2D at 0x15391cd6160>,
 <matplotlib.lines.Line2D at 0x15391cd6430>,
 <matplotlib.lines.Line2D at 0x15391cd6c10>,
 <matplotlib.lines.Line2D at 0x15391cd6be0>,
 <matplotlib.lines.Line2D at 0x15391cd69a0>,
 <matplotlib.lines.Line2D at 0x15391cd61f0>,
 <matplotlib.lines.Line2D at 0x15391cd6850>,
 <matplotlib.lines.Line2D at 0x15391cd6fd0>,
 <matplotlib.lines.Line2D at 0x15391cd6fa0>,
 <matplotlib.lines.Line2D at 0x15391bd9490>,
 <matplotlib.lines.Line2D at 0x15391bd94c0>,
 <matplotlib.lines.Line2D at 0x15391bd9880>,
 <matplotlib.lines.Line2D at 0x15391bd9580>,
 <matplotlib.lines.Line2D at 0x15391bd9700>,
 <matplotlib.lines.Line2D at 0x15391bd9ca0>,
 <matplotlib.lines.Line2D at 0x15391bd9280>,
 <matplotlib.lines.Line2D at 0x15391bd9d30>,
 <matplotlib.lines.Line2D at 0x15391bd90a0>,
 <matplotlib.lines.Line2D at 0x15391bd9850>,
 <matplotlib.lines.Line2D at 0x15391bd9430>,
 <matplotlib.lines.Line2D at 0x15391bd9820>]

5) Plot the time trajectories of the mean and median wealth at every time point from 0 to 1,000. Try both linear and logarithmic scaler for the wealth axis. What are your observations?

In [11]:
mean_median_df = df1.copy()
w = 100

df1['mean'] = df1.iloc[:, w:2*w].mean(axis=1)
df1['median'] = df1.iloc[:, w:2*w].median(axis=1)
df1
Out[11]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... balance 92 balance 93 balance 94 balance 95 balance 96 balance 97 balance 98 balance 99 mean median
0 1 0 1 1 0 1 0 1 1 0 ... 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02 1.000000e+02
1 0 1 0 0 0 1 0 0 0 1 ... 6.000000e+01 6.000000e+01 1.500000e+02 6.000000e+01 1.500000e+02 1.500000e+02 6.000000e+01 1.500000e+02 1.167000e+02 1.500000e+02
2 1 1 0 1 0 1 1 1 0 0 ... 3.600000e+01 9.000000e+01 9.000000e+01 3.600000e+01 9.000000e+01 9.000000e+01 9.000000e+01 9.000000e+01 1.116000e+02 9.000000e+01
3 0 0 0 0 1 0 0 0 1 1 ... 5.400000e+01 5.400000e+01 1.350000e+02 5.400000e+01 1.350000e+02 5.400000e+01 5.400000e+01 1.350000e+02 1.230120e+02 1.350000e+02
4 0 1 0 0 1 0 1 1 1 1 ... 3.240000e+01 3.240000e+01 8.100000e+01 8.100000e+01 2.025000e+02 3.240000e+01 8.100000e+01 8.100000e+01 1.225287e+02 8.100000e+01
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
995 0 0 0 0 1 0 0 1 0 1 ... 1.114239e-23 5.018087e-34 2.720310e-21 6.333716e-15 6.485725e-17 2.533486e-15 7.131130e-25 1.037716e-17 2.070404e-08 4.760543e-21
996 0 1 1 0 0 1 0 1 1 1 ... 1.671359e-23 3.010852e-34 4.080465e-21 3.800230e-15 9.728588e-17 1.520092e-15 4.278678e-25 1.556574e-17 1.793922e-08 4.080465e-21
997 0 0 0 0 0 1 1 1 0 0 ... 2.507038e-23 1.806511e-34 6.120698e-21 5.700344e-15 1.459288e-16 2.280138e-15 6.418017e-25 2.334861e-17 1.862089e-08 4.284489e-21
998 1 0 0 1 0 0 0 0 1 1 ... 3.760557e-23 2.709767e-34 9.181047e-21 8.550517e-15 8.755729e-17 1.368083e-15 9.627026e-25 1.400917e-17 1.626547e-08 6.426733e-21
999 1 0 1 1 1 1 0 1 0 1 ... 2.256334e-23 4.064650e-34 1.377157e-20 5.130310e-15 1.313359e-16 2.052124e-15 1.444054e-24 8.405500e-18 9.938575e-09 5.508628e-21

1000 rows × 202 columns

In [12]:
df1['mean'].plot()
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
plt.show()
In [13]:
df1['median'].plot()
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
plt.show()

6) Repeat steps 3-5 with N=10 and w=1,000 with the following logic: image.png

In [14]:
n = 10
w = 1000

df2 = pd.DataFrame()
for i in range(1000):
    data = np.random.randint(0, 2, size=n)
    temp_df = pd.DataFrame(data, columns=[f'prob_{i}'])
    df2 = pd.concat([df2, temp_df], axis=1)

for x in range(0, w):
    data = [100] * n
    temp_df = pd.DataFrame(data, columns=[f'balance {x}'])
    df2 = pd.concat([df2, temp_df], axis=1)

for i in range(1,n):
    for j in range(w, 2*w):
        prob_value = df2.iloc[i-1,j-1000]
        if prob_value == 1:
            df2.iloc[i,j] = df2.iloc[i-1,j] + 50
        else:
            df2.iloc[i,j] = df2.iloc[i-1,j] - 40

df2.to_csv('df2.csv')
df2
Out[14]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... balance 990 balance 991 balance 992 balance 993 balance 994 balance 995 balance 996 balance 997 balance 998 balance 999
0 0 1 1 0 0 1 0 0 0 1 ... 100 100 100 100 100 100 100 100 100 100
1 0 0 1 0 0 1 0 0 0 0 ... 60 150 150 150 60 150 150 150 150 60
2 0 0 0 0 0 1 0 1 0 0 ... 110 110 200 200 110 200 110 200 110 20
3 1 0 0 1 0 0 1 1 0 1 ... 160 70 250 160 160 160 160 250 70 -20
4 0 1 1 1 0 1 0 0 0 1 ... 120 30 210 210 120 120 120 210 30 -60
5 0 1 1 0 0 1 0 1 0 0 ... 170 80 260 170 170 80 170 170 80 -10
6 1 0 1 0 1 0 0 1 0 1 ... 220 130 220 130 220 130 130 220 40 -50
7 1 1 0 0 1 1 0 1 1 1 ... 270 90 180 90 270 90 90 270 90 -90
8 1 0 1 0 0 1 1 1 1 0 ... 320 140 140 140 320 50 140 230 140 -130
9 1 1 0 1 1 1 1 0 0 0 ... 280 100 190 100 280 100 100 190 100 -80

10 rows × 2000 columns

In [15]:
count = 0

for i in range(1000,2000):
    if df2.iloc[-1,i] > 1000:
        count += 1

print(f'Number of gambler whose wealth is more than $1000 : {count}')
Number of gambler whose wealth is more than $1000 : 0
In [16]:
for i in range(100,200):
    temp_df = df2.iloc[:,[i]].copy()
    plt.plot(temp_df)
    plt.title(df2.columns[i])
    plt.xlabel('Time in gamble rounds')
    plt.ylabel('Wealth')
    plt.show()
In [17]:
plt.figure(figsize=(12, 12))
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
display(plt.plot(df2))
[<matplotlib.lines.Line2D at 0x15391b6c760>,
 <matplotlib.lines.Line2D at 0x15391f74190>,
 <matplotlib.lines.Line2D at 0x15391c1d220>,
 <matplotlib.lines.Line2D at 0x15391c0bca0>,
 <matplotlib.lines.Line2D at 0x15391bc2610>,
 <matplotlib.lines.Line2D at 0x15391bc2910>,
 <matplotlib.lines.Line2D at 0x15391bc24c0>,
 <matplotlib.lines.Line2D at 0x15391bc2640>,
 <matplotlib.lines.Line2D at 0x15391bc2940>,
 <matplotlib.lines.Line2D at 0x15391bc2490>,
 <matplotlib.lines.Line2D at 0x15391b6c220>,
 <matplotlib.lines.Line2D at 0x15391bc28e0>,
 <matplotlib.lines.Line2D at 0x15391bc2dc0>,
 <matplotlib.lines.Line2D at 0x15391bc2e80>,
 <matplotlib.lines.Line2D at 0x15391bc22b0>,
 <matplotlib.lines.Line2D at 0x15391bc2a00>,
 <matplotlib.lines.Line2D at 0x15391bc21c0>,
 <matplotlib.lines.Line2D at 0x15391bc2af0>,
 <matplotlib.lines.Line2D at 0x153921245b0>,
 <matplotlib.lines.Line2D at 0x15392124610>,
 <matplotlib.lines.Line2D at 0x15392124550>,
 <matplotlib.lines.Line2D at 0x15392124250>,
 <matplotlib.lines.Line2D at 0x15392124070>,
 <matplotlib.lines.Line2D at 0x15392124ee0>,
 <matplotlib.lines.Line2D at 0x15392124280>,
 <matplotlib.lines.Line2D at 0x15392124820>,
 <matplotlib.lines.Line2D at 0x15392124850>,
 <matplotlib.lines.Line2D at 0x153921246d0>,
 <matplotlib.lines.Line2D at 0x15392124580>,
 <matplotlib.lines.Line2D at 0x15392124af0>,
 <matplotlib.lines.Line2D at 0x15392124460>,
 <matplotlib.lines.Line2D at 0x15391b4ffd0>,
 <matplotlib.lines.Line2D at 0x15391b4f070>,
 <matplotlib.lines.Line2D at 0x15391b4f880>,
 <matplotlib.lines.Line2D at 0x15391b4f0a0>,
 <matplotlib.lines.Line2D at 0x15391b4f580>,
 <matplotlib.lines.Line2D at 0x15391b4f490>,
 <matplotlib.lines.Line2D at 0x15391b4f370>,
 <matplotlib.lines.Line2D at 0x15391b4f760>,
 <matplotlib.lines.Line2D at 0x15391b4f820>,
 <matplotlib.lines.Line2D at 0x15391b4f1c0>,
 <matplotlib.lines.Line2D at 0x15391b4f400>,
 <matplotlib.lines.Line2D at 0x15391b4fd90>,
 <matplotlib.lines.Line2D at 0x15391b4f280>,
 <matplotlib.lines.Line2D at 0x15391b4f1f0>,
 <matplotlib.lines.Line2D at 0x15391c57370>,
 <matplotlib.lines.Line2D at 0x15391c578b0>,
 <matplotlib.lines.Line2D at 0x15391c57e50>,
 <matplotlib.lines.Line2D at 0x15391c57cd0>,
 <matplotlib.lines.Line2D at 0x15391c57790>,
 <matplotlib.lines.Line2D at 0x15391c57640>,
 <matplotlib.lines.Line2D at 0x15391c57c40>,
 <matplotlib.lines.Line2D at 0x15391c575e0>,
 <matplotlib.lines.Line2D at 0x15391c57940>,
 <matplotlib.lines.Line2D at 0x15391c57a30>,
 <matplotlib.lines.Line2D at 0x15391c57b50>,
 <matplotlib.lines.Line2D at 0x15391b59520>,
 <matplotlib.lines.Line2D at 0x15391b59b20>,
 <matplotlib.lines.Line2D at 0x15391b59fd0>,
 <matplotlib.lines.Line2D at 0x15391b59280>,
 <matplotlib.lines.Line2D at 0x15391b59130>,
 <matplotlib.lines.Line2D at 0x15391b59700>,
 <matplotlib.lines.Line2D at 0x15391b59dc0>,
 <matplotlib.lines.Line2D at 0x15391b59550>,
 <matplotlib.lines.Line2D at 0x15391b59850>,
 <matplotlib.lines.Line2D at 0x15391b59b50>,
 <matplotlib.lines.Line2D at 0x15391b59310>,
 <matplotlib.lines.Line2D at 0x15391b59be0>,
 <matplotlib.lines.Line2D at 0x15391b590a0>,
 <matplotlib.lines.Line2D at 0x15391d53c70>,
 <matplotlib.lines.Line2D at 0x15391d534f0>,
 <matplotlib.lines.Line2D at 0x15391d531f0>,
 <matplotlib.lines.Line2D at 0x15391d53400>,
 <matplotlib.lines.Line2D at 0x15391d53190>,
 <matplotlib.lines.Line2D at 0x15391d53700>,
 <matplotlib.lines.Line2D at 0x15391d53df0>,
 <matplotlib.lines.Line2D at 0x15391d53880>,
 <matplotlib.lines.Line2D at 0x15391d538e0>,
 <matplotlib.lines.Line2D at 0x15391d53490>,
 <matplotlib.lines.Line2D at 0x15391d53790>,
 <matplotlib.lines.Line2D at 0x15391d53370>,
 <matplotlib.lines.Line2D at 0x15391d53c40>,
 <matplotlib.lines.Line2D at 0x15391d53040>,
 <matplotlib.lines.Line2D at 0x15391b0b160>,
 <matplotlib.lines.Line2D at 0x15391b0b100>,
 <matplotlib.lines.Line2D at 0x15391b0b220>,
 <matplotlib.lines.Line2D at 0x15391b0b760>,
 <matplotlib.lines.Line2D at 0x15391b0ba00>,
 <matplotlib.lines.Line2D at 0x15391b0bb80>,
 <matplotlib.lines.Line2D at 0x15391b0bd90>,
 <matplotlib.lines.Line2D at 0x15391b0bb50>,
 <matplotlib.lines.Line2D at 0x15391b0bd60>,
 <matplotlib.lines.Line2D at 0x15391b0b9d0>,
 <matplotlib.lines.Line2D at 0x15391b0ba30>,
 <matplotlib.lines.Line2D at 0x15391b0b8b0>,
 <matplotlib.lines.Line2D at 0x15391b0b700>,
 <matplotlib.lines.Line2D at 0x15391b0bdc0>,
 <matplotlib.lines.Line2D at 0x15391a9a220>,
 <matplotlib.lines.Line2D at 0x15391a9ac40>,
 <matplotlib.lines.Line2D at 0x15391a9af70>,
 <matplotlib.lines.Line2D at 0x15391a9a070>,
 <matplotlib.lines.Line2D at 0x15391a9ab20>,
 <matplotlib.lines.Line2D at 0x15391a9a1f0>,
 <matplotlib.lines.Line2D at 0x15391a9a370>,
 <matplotlib.lines.Line2D at 0x15391a9ae20>,
 <matplotlib.lines.Line2D at 0x15391a9a3a0>,
 <matplotlib.lines.Line2D at 0x15391a9adc0>,
 <matplotlib.lines.Line2D at 0x15391a9a610>,
 <matplotlib.lines.Line2D at 0x15391a9a5e0>,
 <matplotlib.lines.Line2D at 0x15391a9a880>,
 <matplotlib.lines.Line2D at 0x15391a9ad30>,
 <matplotlib.lines.Line2D at 0x15391d28c40>,
 <matplotlib.lines.Line2D at 0x15391d28e50>,
 <matplotlib.lines.Line2D at 0x15391d28a90>,
 <matplotlib.lines.Line2D at 0x15391d28610>,
 <matplotlib.lines.Line2D at 0x15391d28be0>,
 <matplotlib.lines.Line2D at 0x15391d28bb0>,
 <matplotlib.lines.Line2D at 0x15391d28220>,
 <matplotlib.lines.Line2D at 0x15391d28970>,
 <matplotlib.lines.Line2D at 0x15391d28250>,
 <matplotlib.lines.Line2D at 0x15391d28880>,
 <matplotlib.lines.Line2D at 0x15391d28340>,
 <matplotlib.lines.Line2D at 0x15391d28400>,
 <matplotlib.lines.Line2D at 0x15391d28ca0>,
 <matplotlib.lines.Line2D at 0x15391d28310>,
 <matplotlib.lines.Line2D at 0x15391d6f850>,
 <matplotlib.lines.Line2D at 0x15391d6f610>,
 <matplotlib.lines.Line2D at 0x15391d6f340>,
 <matplotlib.lines.Line2D at 0x15391d6f940>,
 <matplotlib.lines.Line2D at 0x15391d6fa00>,
 <matplotlib.lines.Line2D at 0x15391d6f130>,
 <matplotlib.lines.Line2D at 0x15391d6f490>,
 <matplotlib.lines.Line2D at 0x15391d6f310>,
 <matplotlib.lines.Line2D at 0x15391d6f2e0>,
 <matplotlib.lines.Line2D at 0x15391d6f0a0>,
 <matplotlib.lines.Line2D at 0x15391d6f5b0>,
 <matplotlib.lines.Line2D at 0x15391d6f4c0>,
 <matplotlib.lines.Line2D at 0x15391d6fd00>,
 <matplotlib.lines.Line2D at 0x15391a0dca0>,
 <matplotlib.lines.Line2D at 0x15391a0de80>,
 <matplotlib.lines.Line2D at 0x15391a0db50>,
 <matplotlib.lines.Line2D at 0x15391a0dac0>,
 <matplotlib.lines.Line2D at 0x15391a0df70>,
 <matplotlib.lines.Line2D at 0x15391a0dc10>,
 <matplotlib.lines.Line2D at 0x15391a0d4c0>,
 <matplotlib.lines.Line2D at 0x15391a0dbb0>,
 <matplotlib.lines.Line2D at 0x15391a0d3d0>,
 <matplotlib.lines.Line2D at 0x15391a0df10>,
 <matplotlib.lines.Line2D at 0x15391a0ddf0>,
 <matplotlib.lines.Line2D at 0x15391a0d220>,
 <matplotlib.lines.Line2D at 0x15391a0d8b0>,
 <matplotlib.lines.Line2D at 0x15391a0dd90>,
 <matplotlib.lines.Line2D at 0x15391a75310>,
 <matplotlib.lines.Line2D at 0x15391a75490>,
 <matplotlib.lines.Line2D at 0x15391a75400>,
 <matplotlib.lines.Line2D at 0x15391a75520>,
 <matplotlib.lines.Line2D at 0x15391a75a90>,
 <matplotlib.lines.Line2D at 0x15391a75670>,
 <matplotlib.lines.Line2D at 0x15391a75250>,
 <matplotlib.lines.Line2D at 0x15391a75880>,
 <matplotlib.lines.Line2D at 0x15391a75820>,
 <matplotlib.lines.Line2D at 0x15391a75940>,
 <matplotlib.lines.Line2D at 0x15391a75340>,
 <matplotlib.lines.Line2D at 0x15391a750d0>,
 <matplotlib.lines.Line2D at 0x15391a75130>,
 <matplotlib.lines.Line2D at 0x15391a75610>,
 <matplotlib.lines.Line2D at 0x15391a68640>,
 <matplotlib.lines.Line2D at 0x15391a689a0>,
 <matplotlib.lines.Line2D at 0x15391a68340>,
 <matplotlib.lines.Line2D at 0x15391a68be0>,
 <matplotlib.lines.Line2D at 0x15391a688b0>,
 <matplotlib.lines.Line2D at 0x15391a687c0>,
 <matplotlib.lines.Line2D at 0x15391a68910>,
 <matplotlib.lines.Line2D at 0x15391a68700>,
 <matplotlib.lines.Line2D at 0x15391a68550>,
 <matplotlib.lines.Line2D at 0x15391a68f70>,
 <matplotlib.lines.Line2D at 0x15391a68130>,
 <matplotlib.lines.Line2D at 0x15391a68400>,
 <matplotlib.lines.Line2D at 0x15391a68490>,
 <matplotlib.lines.Line2D at 0x15391a68f10>,
 <matplotlib.lines.Line2D at 0x15391e32130>,
 <matplotlib.lines.Line2D at 0x15391e32730>,
 <matplotlib.lines.Line2D at 0x15391e32850>,
 <matplotlib.lines.Line2D at 0x15391e328e0>,
 <matplotlib.lines.Line2D at 0x15391e322b0>,
 <matplotlib.lines.Line2D at 0x15391e32490>,
 <matplotlib.lines.Line2D at 0x15391e32c10>,
 <matplotlib.lines.Line2D at 0x15391e32f10>,
 <matplotlib.lines.Line2D at 0x15391e329d0>,
 <matplotlib.lines.Line2D at 0x15391e32790>,
 <matplotlib.lines.Line2D at 0x15391e32d30>,
 <matplotlib.lines.Line2D at 0x15391e32b80>,
 <matplotlib.lines.Line2D at 0x15391e329a0>,
 <matplotlib.lines.Line2D at 0x15391d92340>,
 <matplotlib.lines.Line2D at 0x15391d92d90>,
 <matplotlib.lines.Line2D at 0x15391d92820>,
 <matplotlib.lines.Line2D at 0x15391d926d0>,
 <matplotlib.lines.Line2D at 0x15391d92d30>,
 <matplotlib.lines.Line2D at 0x15391d92d00>,
 <matplotlib.lines.Line2D at 0x15391d927f0>,
 <matplotlib.lines.Line2D at 0x15391d92fa0>,
 <matplotlib.lines.Line2D at 0x15391d92dc0>,
 <matplotlib.lines.Line2D at 0x15391d92490>,
 <matplotlib.lines.Line2D at 0x15391d92f10>,
 <matplotlib.lines.Line2D at 0x15391d92610>,
 <matplotlib.lines.Line2D at 0x15391d92ee0>,
 <matplotlib.lines.Line2D at 0x15391d924c0>,
 <matplotlib.lines.Line2D at 0x15391d9b820>,
 <matplotlib.lines.Line2D at 0x15391d9bc10>,
 <matplotlib.lines.Line2D at 0x15391d9b250>,
 <matplotlib.lines.Line2D at 0x15391d9b400>,
 <matplotlib.lines.Line2D at 0x15391d9bc70>,
 <matplotlib.lines.Line2D at 0x15391d9bdf0>,
 <matplotlib.lines.Line2D at 0x15391d9b1f0>,
 <matplotlib.lines.Line2D at 0x15391d9bbe0>,
 <matplotlib.lines.Line2D at 0x15391d9bc40>,
 <matplotlib.lines.Line2D at 0x15391d9b0d0>,
 <matplotlib.lines.Line2D at 0x15391d9bf70>,
 <matplotlib.lines.Line2D at 0x15391d9b730>,
 <matplotlib.lines.Line2D at 0x15391d9bb20>,
 <matplotlib.lines.Line2D at 0x15391d9b880>,
 <matplotlib.lines.Line2D at 0x15391b68220>,
 <matplotlib.lines.Line2D at 0x15391b68790>,
 <matplotlib.lines.Line2D at 0x15391b681c0>,
 <matplotlib.lines.Line2D at 0x15391b68df0>,
 <matplotlib.lines.Line2D at 0x15391b68c10>,
 <matplotlib.lines.Line2D at 0x15391b683d0>,
 <matplotlib.lines.Line2D at 0x15391b68fd0>,
 <matplotlib.lines.Line2D at 0x15391b686d0>,
 <matplotlib.lines.Line2D at 0x15391b68340>,
 <matplotlib.lines.Line2D at 0x15391b68e50>,
 <matplotlib.lines.Line2D at 0x15391b683a0>,
 <matplotlib.lines.Line2D at 0x15391b680a0>,
 <matplotlib.lines.Line2D at 0x15391b68460>,
 <matplotlib.lines.Line2D at 0x15391b68dc0>,
 <matplotlib.lines.Line2D at 0x15391f83400>,
 <matplotlib.lines.Line2D at 0x15391f83190>,
 <matplotlib.lines.Line2D at 0x15391f83f40>,
 <matplotlib.lines.Line2D at 0x15391f83c10>,
 <matplotlib.lines.Line2D at 0x15391f83fa0>,
 <matplotlib.lines.Line2D at 0x15391f83d30>,
 <matplotlib.lines.Line2D at 0x15391f830d0>,
 <matplotlib.lines.Line2D at 0x15391f839a0>,
 <matplotlib.lines.Line2D at 0x15391f83880>,
 <matplotlib.lines.Line2D at 0x15391f83c70>,
 <matplotlib.lines.Line2D at 0x15391f83a60>,
 <matplotlib.lines.Line2D at 0x15391f83c40>,
 <matplotlib.lines.Line2D at 0x15391c78bb0>,
 <matplotlib.lines.Line2D at 0x15391c78b20>,
 <matplotlib.lines.Line2D at 0x15391c786d0>,
 <matplotlib.lines.Line2D at 0x15391c788e0>,
 <matplotlib.lines.Line2D at 0x15391c787c0>,
 <matplotlib.lines.Line2D at 0x15391c78730>,
 <matplotlib.lines.Line2D at 0x15391c78af0>,
 <matplotlib.lines.Line2D at 0x15391c78f70>,
 <matplotlib.lines.Line2D at 0x15391c78970>,
 <matplotlib.lines.Line2D at 0x15391c785b0>,
 <matplotlib.lines.Line2D at 0x15391c780a0>,
 <matplotlib.lines.Line2D at 0x15391c78490>,
 <matplotlib.lines.Line2D at 0x15391c78760>,
 <matplotlib.lines.Line2D at 0x15391a31820>,
 <matplotlib.lines.Line2D at 0x15391a31550>,
 <matplotlib.lines.Line2D at 0x15391a31af0>,
 <matplotlib.lines.Line2D at 0x15391a31490>,
 <matplotlib.lines.Line2D at 0x15391a31be0>,
 <matplotlib.lines.Line2D at 0x15391a31910>,
 <matplotlib.lines.Line2D at 0x15391a31f40>,
 <matplotlib.lines.Line2D at 0x15391a31940>,
 <matplotlib.lines.Line2D at 0x15391a31970>,
 <matplotlib.lines.Line2D at 0x15391a31e50>,
 <matplotlib.lines.Line2D at 0x15391a31310>,
 <matplotlib.lines.Line2D at 0x15391a31280>,
 <matplotlib.lines.Line2D at 0x15391a31f70>,
 <matplotlib.lines.Line2D at 0x15391a313d0>,
 <matplotlib.lines.Line2D at 0x153902a6250>,
 <matplotlib.lines.Line2D at 0x153902a6280>,
 <matplotlib.lines.Line2D at 0x153902a6ac0>,
 <matplotlib.lines.Line2D at 0x153902a6b50>,
 <matplotlib.lines.Line2D at 0x15391bf7430>,
 <matplotlib.lines.Line2D at 0x153902a6520>,
 <matplotlib.lines.Line2D at 0x153902a66a0>,
 <matplotlib.lines.Line2D at 0x153902a60d0>,
 <matplotlib.lines.Line2D at 0x153902a67c0>,
 <matplotlib.lines.Line2D at 0x153902a6880>,
 <matplotlib.lines.Line2D at 0x153902a6c40>,
 <matplotlib.lines.Line2D at 0x153902a6550>,
 <matplotlib.lines.Line2D at 0x153909a4eb0>,
 <matplotlib.lines.Line2D at 0x153909a40d0>,
 <matplotlib.lines.Line2D at 0x153909a49d0>,
 <matplotlib.lines.Line2D at 0x153909a4460>,
 <matplotlib.lines.Line2D at 0x153909a4f10>,
 <matplotlib.lines.Line2D at 0x153909a4280>,
 <matplotlib.lines.Line2D at 0x153909a46d0>,
 <matplotlib.lines.Line2D at 0x153909a4e50>,
 <matplotlib.lines.Line2D at 0x153909a4c40>,
 <matplotlib.lines.Line2D at 0x153909a4b80>,
 <matplotlib.lines.Line2D at 0x153909a4850>,
 <matplotlib.lines.Line2D at 0x153909a4130>,
 <matplotlib.lines.Line2D at 0x153909a4f40>,
 <matplotlib.lines.Line2D at 0x15391daa340>,
 <matplotlib.lines.Line2D at 0x15391daae80>,
 <matplotlib.lines.Line2D at 0x15391daaa90>,
 <matplotlib.lines.Line2D at 0x15391daaac0>,
 <matplotlib.lines.Line2D at 0x15391daac70>,
 <matplotlib.lines.Line2D at 0x15391daaf70>,
 <matplotlib.lines.Line2D at 0x15391daad30>,
 <matplotlib.lines.Line2D at 0x15391daaf40>,
 <matplotlib.lines.Line2D at 0x15391daa4f0>,
 <matplotlib.lines.Line2D at 0x15391daab50>,
 <matplotlib.lines.Line2D at 0x15391daa430>,
 <matplotlib.lines.Line2D at 0x15391daa1f0>,
 <matplotlib.lines.Line2D at 0x15391daaa60>,
 <matplotlib.lines.Line2D at 0x15391daadf0>,
 <matplotlib.lines.Line2D at 0x15391af7250>,
 <matplotlib.lines.Line2D at 0x15391af7e20>,
 <matplotlib.lines.Line2D at 0x15391af7b50>,
 <matplotlib.lines.Line2D at 0x15391af7160>,
 <matplotlib.lines.Line2D at 0x15391af7ac0>,
 <matplotlib.lines.Line2D at 0x15391af7b20>,
 <matplotlib.lines.Line2D at 0x15391af7760>,
 <matplotlib.lines.Line2D at 0x15391af7220>,
 <matplotlib.lines.Line2D at 0x15391af7190>,
 <matplotlib.lines.Line2D at 0x15391af7d00>,
 <matplotlib.lines.Line2D at 0x15391af7be0>,
 <matplotlib.lines.Line2D at 0x15391af7df0>,
 <matplotlib.lines.Line2D at 0x15391af7d90>,
 <matplotlib.lines.Line2D at 0x15391af7100>,
 <matplotlib.lines.Line2D at 0x15391c595e0>,
 <matplotlib.lines.Line2D at 0x15391c590a0>,
 <matplotlib.lines.Line2D at 0x15391c59580>,
 <matplotlib.lines.Line2D at 0x15391c599a0>,
 <matplotlib.lines.Line2D at 0x15391c59d90>,
 <matplotlib.lines.Line2D at 0x15391c59b80>,
 <matplotlib.lines.Line2D at 0x15391c59850>,
 <matplotlib.lines.Line2D at 0x15391c59fa0>,
 <matplotlib.lines.Line2D at 0x15391c59fd0>,
 <matplotlib.lines.Line2D at 0x15391c59a30>,
 <matplotlib.lines.Line2D at 0x15391c598b0>,
 <matplotlib.lines.Line2D at 0x15391c59d30>,
 <matplotlib.lines.Line2D at 0x15391c59310>,
 <matplotlib.lines.Line2D at 0x15391d5cd60>,
 <matplotlib.lines.Line2D at 0x15391d5c100>,
 <matplotlib.lines.Line2D at 0x15391d5cc40>,
 <matplotlib.lines.Line2D at 0x15391d5c280>,
 <matplotlib.lines.Line2D at 0x15391d5ca30>,
 <matplotlib.lines.Line2D at 0x15391d5c9d0>,
 <matplotlib.lines.Line2D at 0x15391d5c7c0>,
 <matplotlib.lines.Line2D at 0x15391d5c370>,
 <matplotlib.lines.Line2D at 0x15391d5cb20>,
 <matplotlib.lines.Line2D at 0x15391d5c3a0>,
 <matplotlib.lines.Line2D at 0x15391d5c5b0>,
 <matplotlib.lines.Line2D at 0x15391d5c070>,
 <matplotlib.lines.Line2D at 0x15391d5c8e0>,
 <matplotlib.lines.Line2D at 0x15391d5c6a0>,
 <matplotlib.lines.Line2D at 0x15391edc100>,
 <matplotlib.lines.Line2D at 0x15391edc520>,
 <matplotlib.lines.Line2D at 0x15391edc8e0>,
 <matplotlib.lines.Line2D at 0x15391edc5e0>,
 <matplotlib.lines.Line2D at 0x15391edc1c0>,
 <matplotlib.lines.Line2D at 0x15391edc310>,
 <matplotlib.lines.Line2D at 0x15391edcf70>,
 <matplotlib.lines.Line2D at 0x15391f56c10>,
 <matplotlib.lines.Line2D at 0x15391f56460>,
 <matplotlib.lines.Line2D at 0x15391d06ac0>,
 <matplotlib.lines.Line2D at 0x15391edc460>,
 <matplotlib.lines.Line2D at 0x15391edc6d0>,
 <matplotlib.lines.Line2D at 0x15391edc070>,
 <matplotlib.lines.Line2D at 0x15391edc220>,
 <matplotlib.lines.Line2D at 0x15391edc0a0>,
 <matplotlib.lines.Line2D at 0x15391edc250>,
 <matplotlib.lines.Line2D at 0x15391b692e0>,
 <matplotlib.lines.Line2D at 0x15391b692b0>,
 <matplotlib.lines.Line2D at 0x15391b69670>,
 <matplotlib.lines.Line2D at 0x15391b697f0>,
 <matplotlib.lines.Line2D at 0x15391b69dc0>,
 <matplotlib.lines.Line2D at 0x15391b698e0>,
 <matplotlib.lines.Line2D at 0x15391b69880>,
 <matplotlib.lines.Line2D at 0x15391b69760>,
 <matplotlib.lines.Line2D at 0x15391b699d0>,
 <matplotlib.lines.Line2D at 0x15391b69f70>,
 <matplotlib.lines.Line2D at 0x15391b69d30>,
 <matplotlib.lines.Line2D at 0x15391b69bb0>,
 <matplotlib.lines.Line2D at 0x15391b693d0>,
 <matplotlib.lines.Line2D at 0x15391bd9580>,
 <matplotlib.lines.Line2D at 0x15391bd9220>,
 <matplotlib.lines.Line2D at 0x15391bd9700>,
 <matplotlib.lines.Line2D at 0x15391bd9f10>,
 <matplotlib.lines.Line2D at 0x15391bd9af0>,
 <matplotlib.lines.Line2D at 0x15391bd98b0>,
 <matplotlib.lines.Line2D at 0x15391bd9790>,
 <matplotlib.lines.Line2D at 0x15391bd9400>,
 <matplotlib.lines.Line2D at 0x15391bd9310>,
 <matplotlib.lines.Line2D at 0x15391bd9a30>,
 <matplotlib.lines.Line2D at 0x15391bd9fa0>,
 <matplotlib.lines.Line2D at 0x15391bd9d30>,
 <matplotlib.lines.Line2D at 0x15391bd99d0>,
 <matplotlib.lines.Line2D at 0x15391bd9eb0>,
 <matplotlib.lines.Line2D at 0x15391b36bb0>,
 <matplotlib.lines.Line2D at 0x15391b365b0>,
 <matplotlib.lines.Line2D at 0x15391b36dc0>,
 <matplotlib.lines.Line2D at 0x15391b36280>,
 <matplotlib.lines.Line2D at 0x15391b368b0>,
 <matplotlib.lines.Line2D at 0x15391b36430>,
 <matplotlib.lines.Line2D at 0x15391b36a30>,
 <matplotlib.lines.Line2D at 0x15391b36400>,
 <matplotlib.lines.Line2D at 0x15391b36ca0>,
 <matplotlib.lines.Line2D at 0x15391b36b50>,
 <matplotlib.lines.Line2D at 0x15391b361c0>,
 <matplotlib.lines.Line2D at 0x15391b36e50>,
 <matplotlib.lines.Line2D at 0x15391b36730>,
 <matplotlib.lines.Line2D at 0x15391cc8be0>,
 <matplotlib.lines.Line2D at 0x15391cc8790>,
 <matplotlib.lines.Line2D at 0x15391cc88e0>,
 <matplotlib.lines.Line2D at 0x15391cc8c40>,
 <matplotlib.lines.Line2D at 0x15391cc8340>,
 <matplotlib.lines.Line2D at 0x15391cc8400>,
 <matplotlib.lines.Line2D at 0x15391cc8070>,
 <matplotlib.lines.Line2D at 0x15391cc86a0>,
 <matplotlib.lines.Line2D at 0x15391cc81f0>,
 <matplotlib.lines.Line2D at 0x15391cc8220>,
 <matplotlib.lines.Line2D at 0x15391cc8d60>,
 <matplotlib.lines.Line2D at 0x15391cc8ca0>,
 <matplotlib.lines.Line2D at 0x15391cc8ac0>,
 <matplotlib.lines.Line2D at 0x15391cc8550>,
 <matplotlib.lines.Line2D at 0x153909d30d0>,
 <matplotlib.lines.Line2D at 0x153909d3190>,
 <matplotlib.lines.Line2D at 0x153909d3970>,
 <matplotlib.lines.Line2D at 0x153909d36d0>,
 <matplotlib.lines.Line2D at 0x153909d3430>,
 <matplotlib.lines.Line2D at 0x153909d3820>,
 <matplotlib.lines.Line2D at 0x153909d38b0>,
 <matplotlib.lines.Line2D at 0x153909d34c0>,
 <matplotlib.lines.Line2D at 0x153909d32b0>,
 <matplotlib.lines.Line2D at 0x153909d3580>,
 <matplotlib.lines.Line2D at 0x15391a50eb0>,
 <matplotlib.lines.Line2D at 0x15391a50940>,
 <matplotlib.lines.Line2D at 0x15391a50190>,
 <matplotlib.lines.Line2D at 0x15391a50100>,
 <matplotlib.lines.Line2D at 0x15391a507f0>,
 <matplotlib.lines.Line2D at 0x15391a500a0>,
 <matplotlib.lines.Line2D at 0x15391a50670>,
 <matplotlib.lines.Line2D at 0x15391a50880>,
 <matplotlib.lines.Line2D at 0x15391a50400>,
 <matplotlib.lines.Line2D at 0x15391a504f0>,
 <matplotlib.lines.Line2D at 0x15391a50640>,
 <matplotlib.lines.Line2D at 0x15391a50c70>,
 <matplotlib.lines.Line2D at 0x15391a501c0>,
 <matplotlib.lines.Line2D at 0x15391ab2340>,
 <matplotlib.lines.Line2D at 0x15391ab2e50>,
 <matplotlib.lines.Line2D at 0x15391ab29d0>,
 <matplotlib.lines.Line2D at 0x15391ab2a30>,
 <matplotlib.lines.Line2D at 0x15391ab2d30>,
 <matplotlib.lines.Line2D at 0x15391ab2040>,
 <matplotlib.lines.Line2D at 0x15391ab2f10>,
 <matplotlib.lines.Line2D at 0x15391ab2c10>,
 <matplotlib.lines.Line2D at 0x15391ab2820>,
 <matplotlib.lines.Line2D at 0x15391ab25b0>,
 <matplotlib.lines.Line2D at 0x15391ab2e20>,
 <matplotlib.lines.Line2D at 0x15391ab2760>,
 <matplotlib.lines.Line2D at 0x15391ab27c0>,
 <matplotlib.lines.Line2D at 0x15391cd6dc0>,
 <matplotlib.lines.Line2D at 0x15391cd6e20>,
 <matplotlib.lines.Line2D at 0x15391cd6310>,
 <matplotlib.lines.Line2D at 0x15391cd6c70>,
 <matplotlib.lines.Line2D at 0x15391cd68b0>,
 <matplotlib.lines.Line2D at 0x15391cd6f70>,
 <matplotlib.lines.Line2D at 0x15391cd6610>,
 <matplotlib.lines.Line2D at 0x15391cd6400>,
 <matplotlib.lines.Line2D at 0x15391cd6af0>,
 <matplotlib.lines.Line2D at 0x15391cd6370>,
 <matplotlib.lines.Line2D at 0x15391cd60a0>,
 <matplotlib.lines.Line2D at 0x15391cd6bb0>,
 <matplotlib.lines.Line2D at 0x15391cd6130>,
 <matplotlib.lines.Line2D at 0x15391cd65b0>,
 <matplotlib.lines.Line2D at 0x15391de8c70>,
 <matplotlib.lines.Line2D at 0x15391de8970>,
 <matplotlib.lines.Line2D at 0x15391de8490>,
 <matplotlib.lines.Line2D at 0x15391de8c40>,
 <matplotlib.lines.Line2D at 0x15391de8a00>,
 <matplotlib.lines.Line2D at 0x15391de88b0>,
 <matplotlib.lines.Line2D at 0x15391de84c0>,
 <matplotlib.lines.Line2D at 0x15391de8130>,
 <matplotlib.lines.Line2D at 0x15391de87c0>,
 <matplotlib.lines.Line2D at 0x15391de8a30>,
 <matplotlib.lines.Line2D at 0x15391de88e0>,
 <matplotlib.lines.Line2D at 0x15391de89a0>,
 <matplotlib.lines.Line2D at 0x15391de85b0>,
 <matplotlib.lines.Line2D at 0x15391de8880>,
 <matplotlib.lines.Line2D at 0x1539212c7f0>,
 <matplotlib.lines.Line2D at 0x1539212c2b0>,
 <matplotlib.lines.Line2D at 0x1539212ce50>,
 <matplotlib.lines.Line2D at 0x1539212cf70>,
 <matplotlib.lines.Line2D at 0x15391ee30d0>,
 <matplotlib.lines.Line2D at 0x15391ee31f0>,
 <matplotlib.lines.Line2D at 0x15391ee3310>,
 <matplotlib.lines.Line2D at 0x15391ee3430>,
 <matplotlib.lines.Line2D at 0x15391ee3550>,
 <matplotlib.lines.Line2D at 0x15391ee3670>,
 <matplotlib.lines.Line2D at 0x15391ee3790>,
 <matplotlib.lines.Line2D at 0x15391ee38b0>,
 <matplotlib.lines.Line2D at 0x15391ee39d0>,
 <matplotlib.lines.Line2D at 0x15391ee3af0>,
 <matplotlib.lines.Line2D at 0x15391ee3c10>,
 <matplotlib.lines.Line2D at 0x15391ee3d30>,
 <matplotlib.lines.Line2D at 0x15391ee3e50>,
 <matplotlib.lines.Line2D at 0x15391ee3f70>,
 <matplotlib.lines.Line2D at 0x15391ec30d0>,
 <matplotlib.lines.Line2D at 0x15391ec31f0>,
 <matplotlib.lines.Line2D at 0x15391ec3310>,
 <matplotlib.lines.Line2D at 0x15391ec3430>,
 <matplotlib.lines.Line2D at 0x15391ec3550>,
 <matplotlib.lines.Line2D at 0x15391ec3670>,
 <matplotlib.lines.Line2D at 0x15391ec3790>,
 <matplotlib.lines.Line2D at 0x15391ec38b0>,
 <matplotlib.lines.Line2D at 0x15391ec39d0>,
 <matplotlib.lines.Line2D at 0x15391ec3af0>,
 <matplotlib.lines.Line2D at 0x15391ec3c10>,
 <matplotlib.lines.Line2D at 0x15391ec3d30>,
 <matplotlib.lines.Line2D at 0x15391ec3e50>,
 <matplotlib.lines.Line2D at 0x15391ec3f70>,
 <matplotlib.lines.Line2D at 0x15391ed40d0>,
 <matplotlib.lines.Line2D at 0x15391ed41f0>,
 <matplotlib.lines.Line2D at 0x15391ed4310>,
 <matplotlib.lines.Line2D at 0x15391ed4430>,
 <matplotlib.lines.Line2D at 0x15391ed4550>,
 <matplotlib.lines.Line2D at 0x15391ed4670>,
 <matplotlib.lines.Line2D at 0x15391ed4790>,
 <matplotlib.lines.Line2D at 0x15391ed48b0>,
 <matplotlib.lines.Line2D at 0x15391ed49d0>,
 <matplotlib.lines.Line2D at 0x15391ed4af0>,
 <matplotlib.lines.Line2D at 0x15391ed4c10>,
 <matplotlib.lines.Line2D at 0x15391ed4d30>,
 <matplotlib.lines.Line2D at 0x15391ed4e50>,
 <matplotlib.lines.Line2D at 0x15391ed4f70>,
 <matplotlib.lines.Line2D at 0x15391ed8310>,
 <matplotlib.lines.Line2D at 0x15391ed84f0>,
 <matplotlib.lines.Line2D at 0x15391ed87c0>,
 <matplotlib.lines.Line2D at 0x15391ed82e0>,
 <matplotlib.lines.Line2D at 0x15391ed8790>,
 <matplotlib.lines.Line2D at 0x15391ed89a0>,
 <matplotlib.lines.Line2D at 0x15391ed8b80>,
 <matplotlib.lines.Line2D at 0x15391ed8ee0>,
 <matplotlib.lines.Line2D at 0x15391ed8bb0>,
 <matplotlib.lines.Line2D at 0x15391ed8dc0>,
 <matplotlib.lines.Line2D at 0x15391ed8df0>,
 <matplotlib.lines.Line2D at 0x15391ed8490>,
 <matplotlib.lines.Line2D at 0x15391ed8d00>,
 <matplotlib.lines.Line2D at 0x15391ed8340>,
 <matplotlib.lines.Line2D at 0x15391eff0d0>,
 <matplotlib.lines.Line2D at 0x15391eff1f0>,
 <matplotlib.lines.Line2D at 0x15391eff310>,
 <matplotlib.lines.Line2D at 0x15391eff430>,
 <matplotlib.lines.Line2D at 0x15391eff550>,
 <matplotlib.lines.Line2D at 0x15391eff670>,
 <matplotlib.lines.Line2D at 0x15391eff790>,
 <matplotlib.lines.Line2D at 0x15391eff8b0>,
 <matplotlib.lines.Line2D at 0x15391eff9d0>,
 <matplotlib.lines.Line2D at 0x15391effaf0>,
 <matplotlib.lines.Line2D at 0x15391effc10>,
 <matplotlib.lines.Line2D at 0x15391effd30>,
 <matplotlib.lines.Line2D at 0x15391effe50>,
 <matplotlib.lines.Line2D at 0x15391efff70>,
 <matplotlib.lines.Line2D at 0x15391efe0d0>,
 <matplotlib.lines.Line2D at 0x15391efe1f0>,
 <matplotlib.lines.Line2D at 0x15391efe310>,
 <matplotlib.lines.Line2D at 0x15391efe430>,
 <matplotlib.lines.Line2D at 0x15391efe550>,
 <matplotlib.lines.Line2D at 0x15391efe670>,
 <matplotlib.lines.Line2D at 0x15391efe790>,
 <matplotlib.lines.Line2D at 0x15391efe8b0>,
 <matplotlib.lines.Line2D at 0x15391efe9d0>,
 <matplotlib.lines.Line2D at 0x15391efeaf0>,
 <matplotlib.lines.Line2D at 0x15391efec10>,
 <matplotlib.lines.Line2D at 0x15391efed30>,
 <matplotlib.lines.Line2D at 0x15391efee50>,
 <matplotlib.lines.Line2D at 0x15391efef70>,
 <matplotlib.lines.Line2D at 0x15391ecc0d0>,
 <matplotlib.lines.Line2D at 0x15391ecc1f0>,
 <matplotlib.lines.Line2D at 0x15391ecc310>,
 <matplotlib.lines.Line2D at 0x15391ecc430>,
 <matplotlib.lines.Line2D at 0x15391ecc550>,
 <matplotlib.lines.Line2D at 0x15391ecc670>,
 <matplotlib.lines.Line2D at 0x15391ecc790>,
 <matplotlib.lines.Line2D at 0x15391ecc8b0>,
 <matplotlib.lines.Line2D at 0x15391ecc9d0>,
 <matplotlib.lines.Line2D at 0x15391eccaf0>,
 <matplotlib.lines.Line2D at 0x15391eccc10>,
 <matplotlib.lines.Line2D at 0x15391eccd30>,
 <matplotlib.lines.Line2D at 0x15391ecce50>,
 <matplotlib.lines.Line2D at 0x15391eccf70>,
 <matplotlib.lines.Line2D at 0x15391ec40d0>,
 <matplotlib.lines.Line2D at 0x15391ec41f0>,
 <matplotlib.lines.Line2D at 0x15391ec4310>,
 <matplotlib.lines.Line2D at 0x15391ec4430>,
 <matplotlib.lines.Line2D at 0x15391ec4550>,
 <matplotlib.lines.Line2D at 0x15391ec4670>,
 <matplotlib.lines.Line2D at 0x15391ec4790>,
 <matplotlib.lines.Line2D at 0x15391ec48b0>,
 <matplotlib.lines.Line2D at 0x15391ec49d0>,
 <matplotlib.lines.Line2D at 0x15391ec4af0>,
 <matplotlib.lines.Line2D at 0x15391ec4c10>,
 <matplotlib.lines.Line2D at 0x15391ec4d30>,
 <matplotlib.lines.Line2D at 0x15391ec4e50>,
 <matplotlib.lines.Line2D at 0x15391ec4f70>,
 <matplotlib.lines.Line2D at 0x15391ee00d0>,
 <matplotlib.lines.Line2D at 0x15391ee01f0>,
 <matplotlib.lines.Line2D at 0x15391ee0310>,
 <matplotlib.lines.Line2D at 0x15391ee0430>,
 <matplotlib.lines.Line2D at 0x15391ee0550>,
 <matplotlib.lines.Line2D at 0x15391ee0670>,
 <matplotlib.lines.Line2D at 0x15391ee0790>,
 <matplotlib.lines.Line2D at 0x15391ee08b0>,
 <matplotlib.lines.Line2D at 0x15391ee09d0>,
 <matplotlib.lines.Line2D at 0x15391ee0af0>,
 <matplotlib.lines.Line2D at 0x15391ee0c10>,
 <matplotlib.lines.Line2D at 0x15391ee0d30>,
 <matplotlib.lines.Line2D at 0x15391ee0e50>,
 <matplotlib.lines.Line2D at 0x15391ee0f70>,
 <matplotlib.lines.Line2D at 0x15391b2d0d0>,
 <matplotlib.lines.Line2D at 0x15391b2d1f0>,
 <matplotlib.lines.Line2D at 0x15391b2d310>,
 <matplotlib.lines.Line2D at 0x15391b2d430>,
 <matplotlib.lines.Line2D at 0x15391b2d550>,
 <matplotlib.lines.Line2D at 0x15391b2d670>,
 <matplotlib.lines.Line2D at 0x15391b2d790>,
 <matplotlib.lines.Line2D at 0x15391b2d8b0>,
 <matplotlib.lines.Line2D at 0x15391b2d9d0>,
 <matplotlib.lines.Line2D at 0x15391b2daf0>,
 <matplotlib.lines.Line2D at 0x15391b2dc10>,
 <matplotlib.lines.Line2D at 0x15391b2dd30>,
 <matplotlib.lines.Line2D at 0x15391b2de50>,
 <matplotlib.lines.Line2D at 0x15391b2df70>,
 <matplotlib.lines.Line2D at 0x15391b260d0>,
 <matplotlib.lines.Line2D at 0x15391b261f0>,
 <matplotlib.lines.Line2D at 0x15391b26310>,
 <matplotlib.lines.Line2D at 0x15391b26430>,
 <matplotlib.lines.Line2D at 0x15391b26550>,
 <matplotlib.lines.Line2D at 0x15391b26670>,
 <matplotlib.lines.Line2D at 0x15391b26790>,
 <matplotlib.lines.Line2D at 0x15391b268b0>,
 <matplotlib.lines.Line2D at 0x15391b269d0>,
 <matplotlib.lines.Line2D at 0x15391b26af0>,
 <matplotlib.lines.Line2D at 0x15391b26c10>,
 <matplotlib.lines.Line2D at 0x15391b26d30>,
 <matplotlib.lines.Line2D at 0x15391b26e50>,
 <matplotlib.lines.Line2D at 0x15391b26f70>,
 <matplotlib.lines.Line2D at 0x15391b250d0>,
 <matplotlib.lines.Line2D at 0x15391b251f0>,
 <matplotlib.lines.Line2D at 0x15391b25310>,
 <matplotlib.lines.Line2D at 0x15391b25430>,
 <matplotlib.lines.Line2D at 0x15391b25550>,
 <matplotlib.lines.Line2D at 0x15391b25670>,
 <matplotlib.lines.Line2D at 0x15391b25790>,
 <matplotlib.lines.Line2D at 0x15391b258b0>,
 <matplotlib.lines.Line2D at 0x15391b259d0>,
 <matplotlib.lines.Line2D at 0x15391b25af0>,
 <matplotlib.lines.Line2D at 0x15391b25c10>,
 <matplotlib.lines.Line2D at 0x15391b25d30>,
 <matplotlib.lines.Line2D at 0x15391b25e50>,
 <matplotlib.lines.Line2D at 0x15391b25f70>,
 <matplotlib.lines.Line2D at 0x15391b2f0d0>,
 <matplotlib.lines.Line2D at 0x15391b2f1f0>,
 <matplotlib.lines.Line2D at 0x15391b2f310>,
 <matplotlib.lines.Line2D at 0x15391b2f430>,
 <matplotlib.lines.Line2D at 0x15391b2f550>,
 <matplotlib.lines.Line2D at 0x15391b2f670>,
 <matplotlib.lines.Line2D at 0x15391b2f790>,
 <matplotlib.lines.Line2D at 0x15391b2f8b0>,
 <matplotlib.lines.Line2D at 0x15391b2f9d0>,
 <matplotlib.lines.Line2D at 0x15391b2faf0>,
 <matplotlib.lines.Line2D at 0x15391b2fc10>,
 <matplotlib.lines.Line2D at 0x15391b2fd30>,
 <matplotlib.lines.Line2D at 0x15391b2fe50>,
 <matplotlib.lines.Line2D at 0x15391b2ff70>,
 <matplotlib.lines.Line2D at 0x15391f5e0d0>,
 <matplotlib.lines.Line2D at 0x15391f5e1f0>,
 <matplotlib.lines.Line2D at 0x15391f5e310>,
 <matplotlib.lines.Line2D at 0x15391f5e430>,
 <matplotlib.lines.Line2D at 0x15391f5e550>,
 <matplotlib.lines.Line2D at 0x15391f5e670>,
 <matplotlib.lines.Line2D at 0x15391f5e790>,
 <matplotlib.lines.Line2D at 0x15391f5e8b0>,
 <matplotlib.lines.Line2D at 0x15391f5e9d0>,
 <matplotlib.lines.Line2D at 0x15391f5eaf0>,
 <matplotlib.lines.Line2D at 0x15391f5ec10>,
 <matplotlib.lines.Line2D at 0x15391f5ed30>,
 <matplotlib.lines.Line2D at 0x15391f5ee50>,
 <matplotlib.lines.Line2D at 0x15391f5ef70>,
 <matplotlib.lines.Line2D at 0x15391f6a0d0>,
 <matplotlib.lines.Line2D at 0x15391f6a1f0>,
 <matplotlib.lines.Line2D at 0x15391f6a310>,
 <matplotlib.lines.Line2D at 0x15391f6a430>,
 <matplotlib.lines.Line2D at 0x15391f6a550>,
 <matplotlib.lines.Line2D at 0x15391f6a670>,
 <matplotlib.lines.Line2D at 0x15391f6a790>,
 <matplotlib.lines.Line2D at 0x15391f6a8b0>,
 <matplotlib.lines.Line2D at 0x15391f6a9d0>,
 <matplotlib.lines.Line2D at 0x15391f6aaf0>,
 <matplotlib.lines.Line2D at 0x15391f6ac10>,
 <matplotlib.lines.Line2D at 0x15391f6ad30>,
 <matplotlib.lines.Line2D at 0x15391f6ae50>,
 <matplotlib.lines.Line2D at 0x15391f6af70>,
 <matplotlib.lines.Line2D at 0x15391f410d0>,
 <matplotlib.lines.Line2D at 0x15391f411f0>,
 <matplotlib.lines.Line2D at 0x15391f41310>,
 <matplotlib.lines.Line2D at 0x15391f41430>,
 <matplotlib.lines.Line2D at 0x15391f41550>,
 <matplotlib.lines.Line2D at 0x15391f41670>,
 <matplotlib.lines.Line2D at 0x15391f41790>,
 <matplotlib.lines.Line2D at 0x15391f418b0>,
 <matplotlib.lines.Line2D at 0x15391f419d0>,
 <matplotlib.lines.Line2D at 0x15391f41af0>,
 <matplotlib.lines.Line2D at 0x15391f41c10>,
 <matplotlib.lines.Line2D at 0x15391f41d30>,
 <matplotlib.lines.Line2D at 0x15391f41e50>,
 <matplotlib.lines.Line2D at 0x15391f41f70>,
 <matplotlib.lines.Line2D at 0x15391f770d0>,
 <matplotlib.lines.Line2D at 0x15391f771f0>,
 <matplotlib.lines.Line2D at 0x15391f77310>,
 <matplotlib.lines.Line2D at 0x15391f77430>,
 <matplotlib.lines.Line2D at 0x15391f77550>,
 <matplotlib.lines.Line2D at 0x15391f77670>,
 <matplotlib.lines.Line2D at 0x15391f77790>,
 <matplotlib.lines.Line2D at 0x15391f778b0>,
 <matplotlib.lines.Line2D at 0x15391f779d0>,
 <matplotlib.lines.Line2D at 0x15391f77af0>,
 <matplotlib.lines.Line2D at 0x15391f77c10>,
 <matplotlib.lines.Line2D at 0x15391f77d30>,
 <matplotlib.lines.Line2D at 0x15391f77e50>,
 <matplotlib.lines.Line2D at 0x15391f77f70>,
 <matplotlib.lines.Line2D at 0x15391f4c0d0>,
 <matplotlib.lines.Line2D at 0x15391f4c1f0>,
 <matplotlib.lines.Line2D at 0x15391f4c310>,
 <matplotlib.lines.Line2D at 0x15391f4c430>,
 <matplotlib.lines.Line2D at 0x15391f4c550>,
 <matplotlib.lines.Line2D at 0x15391f4c670>,
 <matplotlib.lines.Line2D at 0x15391f4c790>,
 <matplotlib.lines.Line2D at 0x15391f4c8b0>,
 <matplotlib.lines.Line2D at 0x15391f4c9d0>,
 <matplotlib.lines.Line2D at 0x15391f4caf0>,
 <matplotlib.lines.Line2D at 0x15391f4cc10>,
 <matplotlib.lines.Line2D at 0x15391f4cd30>,
 <matplotlib.lines.Line2D at 0x15391f4ce50>,
 <matplotlib.lines.Line2D at 0x15391f4cf70>,
 <matplotlib.lines.Line2D at 0x15391e070d0>,
 <matplotlib.lines.Line2D at 0x15391e071f0>,
 <matplotlib.lines.Line2D at 0x15391e07310>,
 <matplotlib.lines.Line2D at 0x15391e07430>,
 <matplotlib.lines.Line2D at 0x15391e07550>,
 <matplotlib.lines.Line2D at 0x15391e07670>,
 <matplotlib.lines.Line2D at 0x15391e07790>,
 <matplotlib.lines.Line2D at 0x15391e078b0>,
 <matplotlib.lines.Line2D at 0x15391e079d0>,
 <matplotlib.lines.Line2D at 0x15391e07af0>,
 <matplotlib.lines.Line2D at 0x15391e07c10>,
 <matplotlib.lines.Line2D at 0x15391e07d30>,
 <matplotlib.lines.Line2D at 0x15391e07e50>,
 <matplotlib.lines.Line2D at 0x15391e07f70>,
 <matplotlib.lines.Line2D at 0x15391e130d0>,
 <matplotlib.lines.Line2D at 0x15391e131f0>,
 <matplotlib.lines.Line2D at 0x15391e13310>,
 <matplotlib.lines.Line2D at 0x15391e13430>,
 <matplotlib.lines.Line2D at 0x15391e13550>,
 <matplotlib.lines.Line2D at 0x15391e13670>,
 <matplotlib.lines.Line2D at 0x15391e13790>,
 <matplotlib.lines.Line2D at 0x15391e138b0>,
 <matplotlib.lines.Line2D at 0x15391e139d0>,
 <matplotlib.lines.Line2D at 0x15391e13af0>,
 <matplotlib.lines.Line2D at 0x15391e13c10>,
 <matplotlib.lines.Line2D at 0x15391e13d30>,
 <matplotlib.lines.Line2D at 0x15391e13e50>,
 <matplotlib.lines.Line2D at 0x15391e13f70>,
 <matplotlib.lines.Line2D at 0x15391e030d0>,
 <matplotlib.lines.Line2D at 0x15391e031f0>,
 <matplotlib.lines.Line2D at 0x15391e03310>,
 <matplotlib.lines.Line2D at 0x15391e03430>,
 <matplotlib.lines.Line2D at 0x15391e03550>,
 <matplotlib.lines.Line2D at 0x15391e03670>,
 <matplotlib.lines.Line2D at 0x15391e03790>,
 <matplotlib.lines.Line2D at 0x15391e038b0>,
 <matplotlib.lines.Line2D at 0x15391e039d0>,
 <matplotlib.lines.Line2D at 0x15391e03af0>,
 <matplotlib.lines.Line2D at 0x15391e03c10>,
 <matplotlib.lines.Line2D at 0x15391e03d30>,
 <matplotlib.lines.Line2D at 0x15391e03e50>,
 <matplotlib.lines.Line2D at 0x15391e03f70>,
 <matplotlib.lines.Line2D at 0x15391e200d0>,
 <matplotlib.lines.Line2D at 0x15391e201f0>,
 <matplotlib.lines.Line2D at 0x15391e20310>,
 <matplotlib.lines.Line2D at 0x15391e20430>,
 <matplotlib.lines.Line2D at 0x15391e20550>,
 <matplotlib.lines.Line2D at 0x15391e20670>,
 <matplotlib.lines.Line2D at 0x15391e20790>,
 <matplotlib.lines.Line2D at 0x15391e208b0>,
 <matplotlib.lines.Line2D at 0x15391e209d0>,
 <matplotlib.lines.Line2D at 0x15391e20af0>,
 <matplotlib.lines.Line2D at 0x15391e20c10>,
 <matplotlib.lines.Line2D at 0x15391e20d30>,
 <matplotlib.lines.Line2D at 0x15391e20e50>,
 <matplotlib.lines.Line2D at 0x15391e20f70>,
 <matplotlib.lines.Line2D at 0x15391bed0d0>,
 <matplotlib.lines.Line2D at 0x15391bed1f0>,
 <matplotlib.lines.Line2D at 0x15391bed310>,
 <matplotlib.lines.Line2D at 0x15391bed430>,
 <matplotlib.lines.Line2D at 0x15391bed550>,
 <matplotlib.lines.Line2D at 0x15391bed670>,
 <matplotlib.lines.Line2D at 0x15391bed790>,
 <matplotlib.lines.Line2D at 0x15391bed8b0>,
 <matplotlib.lines.Line2D at 0x15391bed9d0>,
 <matplotlib.lines.Line2D at 0x15391bedaf0>,
 <matplotlib.lines.Line2D at 0x15391bedc10>,
 <matplotlib.lines.Line2D at 0x15391bedd30>,
 <matplotlib.lines.Line2D at 0x15391bede50>,
 <matplotlib.lines.Line2D at 0x15391bedf70>,
 <matplotlib.lines.Line2D at 0x15391bc00d0>,
 <matplotlib.lines.Line2D at 0x15391bc01f0>,
 <matplotlib.lines.Line2D at 0x15391bc0310>,
 <matplotlib.lines.Line2D at 0x15391bc0430>,
 <matplotlib.lines.Line2D at 0x15391bc0550>,
 <matplotlib.lines.Line2D at 0x15391bc0670>,
 <matplotlib.lines.Line2D at 0x15391bc0790>,
 <matplotlib.lines.Line2D at 0x15391bc08b0>,
 <matplotlib.lines.Line2D at 0x15391bc09d0>,
 <matplotlib.lines.Line2D at 0x15391bc0af0>,
 <matplotlib.lines.Line2D at 0x15391bc0c10>,
 <matplotlib.lines.Line2D at 0x15391bc0d30>,
 <matplotlib.lines.Line2D at 0x15391bc0e50>,
 <matplotlib.lines.Line2D at 0x15391bc0f70>,
 <matplotlib.lines.Line2D at 0x15391bc30d0>,
 <matplotlib.lines.Line2D at 0x15391bc31f0>,
 <matplotlib.lines.Line2D at 0x15391bc3310>,
 <matplotlib.lines.Line2D at 0x15391bc3430>,
 <matplotlib.lines.Line2D at 0x15391bc3550>,
 <matplotlib.lines.Line2D at 0x15391bc3670>,
 <matplotlib.lines.Line2D at 0x15391bc3790>,
 <matplotlib.lines.Line2D at 0x15391bc38b0>,
 <matplotlib.lines.Line2D at 0x15391bc39d0>,
 <matplotlib.lines.Line2D at 0x15391bc3af0>,
 <matplotlib.lines.Line2D at 0x15391bc3c10>,
 <matplotlib.lines.Line2D at 0x15391bc3d30>,
 <matplotlib.lines.Line2D at 0x15391bc3e50>,
 <matplotlib.lines.Line2D at 0x15391bc3f70>,
 <matplotlib.lines.Line2D at 0x15391bf40d0>,
 <matplotlib.lines.Line2D at 0x15391bf41f0>,
 <matplotlib.lines.Line2D at 0x15391bf4310>,
 <matplotlib.lines.Line2D at 0x15391bf4430>,
 <matplotlib.lines.Line2D at 0x15391bf4550>,
 <matplotlib.lines.Line2D at 0x15391bf4670>,
 <matplotlib.lines.Line2D at 0x15391bf4790>,
 <matplotlib.lines.Line2D at 0x15391bf48b0>,
 <matplotlib.lines.Line2D at 0x15391bf49d0>,
 <matplotlib.lines.Line2D at 0x15391bf4af0>,
 <matplotlib.lines.Line2D at 0x15391bf4c10>,
 <matplotlib.lines.Line2D at 0x15391bf4d30>,
 <matplotlib.lines.Line2D at 0x15391bf4e50>,
 <matplotlib.lines.Line2D at 0x15391bf4f70>,
 <matplotlib.lines.Line2D at 0x15391bd20d0>,
 <matplotlib.lines.Line2D at 0x15391bd21f0>,
 <matplotlib.lines.Line2D at 0x15391bd2310>,
 <matplotlib.lines.Line2D at 0x15391bd2430>,
 <matplotlib.lines.Line2D at 0x15391bd2550>,
 <matplotlib.lines.Line2D at 0x15391bd2670>,
 <matplotlib.lines.Line2D at 0x15391bd2790>,
 <matplotlib.lines.Line2D at 0x15391bd28b0>,
 <matplotlib.lines.Line2D at 0x15391bd29d0>,
 <matplotlib.lines.Line2D at 0x15391bd2af0>,
 <matplotlib.lines.Line2D at 0x15391bd2c10>,
 <matplotlib.lines.Line2D at 0x15391bd2d30>,
 <matplotlib.lines.Line2D at 0x15391bd2e50>,
 <matplotlib.lines.Line2D at 0x15391bd2f70>,
 <matplotlib.lines.Line2D at 0x15391cd40d0>,
 <matplotlib.lines.Line2D at 0x15391cd41f0>,
 <matplotlib.lines.Line2D at 0x15391cd4310>,
 <matplotlib.lines.Line2D at 0x15391cd4430>,
 <matplotlib.lines.Line2D at 0x15391cd4550>,
 <matplotlib.lines.Line2D at 0x15391cd4670>,
 <matplotlib.lines.Line2D at 0x15391cd4790>,
 <matplotlib.lines.Line2D at 0x15391cd48b0>,
 <matplotlib.lines.Line2D at 0x15391cd49d0>,
 <matplotlib.lines.Line2D at 0x15391cd4af0>,
 <matplotlib.lines.Line2D at 0x15391cd4c10>,
 <matplotlib.lines.Line2D at 0x15391cd4d30>,
 <matplotlib.lines.Line2D at 0x15391cd4e50>,
 <matplotlib.lines.Line2D at 0x15391cd4f70>,
 <matplotlib.lines.Line2D at 0x15391cca0d0>,
 <matplotlib.lines.Line2D at 0x15391cca1f0>,
 <matplotlib.lines.Line2D at 0x15391cca310>,
 <matplotlib.lines.Line2D at 0x15391cca430>,
 <matplotlib.lines.Line2D at 0x15391cca550>,
 <matplotlib.lines.Line2D at 0x15391cca670>,
 <matplotlib.lines.Line2D at 0x15391cca790>,
 <matplotlib.lines.Line2D at 0x15391cca8b0>,
 <matplotlib.lines.Line2D at 0x15391cca9d0>,
 <matplotlib.lines.Line2D at 0x15391ccaaf0>,
 <matplotlib.lines.Line2D at 0x15391ccac10>,
 <matplotlib.lines.Line2D at 0x15391ccad30>,
 <matplotlib.lines.Line2D at 0x15391ccae50>,
 <matplotlib.lines.Line2D at 0x15391ccaf70>,
 <matplotlib.lines.Line2D at 0x15391ce90d0>,
 <matplotlib.lines.Line2D at 0x15391ce91f0>,
 <matplotlib.lines.Line2D at 0x15391ce9310>,
 <matplotlib.lines.Line2D at 0x15391ce9430>,
 <matplotlib.lines.Line2D at 0x15391ce9550>,
 <matplotlib.lines.Line2D at 0x15391ce9670>,
 <matplotlib.lines.Line2D at 0x15391ce9790>,
 <matplotlib.lines.Line2D at 0x15391ce98b0>,
 <matplotlib.lines.Line2D at 0x15391ce99d0>,
 <matplotlib.lines.Line2D at 0x15391ce9af0>,
 <matplotlib.lines.Line2D at 0x15391ce9c10>,
 <matplotlib.lines.Line2D at 0x15391ce9d30>,
 <matplotlib.lines.Line2D at 0x15391ce9e50>,
 <matplotlib.lines.Line2D at 0x15391ce9f70>,
 <matplotlib.lines.Line2D at 0x15391cdd0d0>,
 <matplotlib.lines.Line2D at 0x15391cdd1f0>,
 <matplotlib.lines.Line2D at 0x15391cdd310>,
 <matplotlib.lines.Line2D at 0x15391cdd430>,
 <matplotlib.lines.Line2D at 0x15391cdd550>,
 <matplotlib.lines.Line2D at 0x15391cdd670>,
 <matplotlib.lines.Line2D at 0x15391cdd790>,
 <matplotlib.lines.Line2D at 0x15391cdd8b0>,
 <matplotlib.lines.Line2D at 0x15391cdd9d0>,
 <matplotlib.lines.Line2D at 0x15391cddaf0>,
 <matplotlib.lines.Line2D at 0x15391cddc10>,
 <matplotlib.lines.Line2D at 0x15391cddd30>,
 <matplotlib.lines.Line2D at 0x15391cdde50>,
 <matplotlib.lines.Line2D at 0x15391cddf70>,
 <matplotlib.lines.Line2D at 0x15391a270d0>,
 <matplotlib.lines.Line2D at 0x15391a271f0>,
 <matplotlib.lines.Line2D at 0x15391a27310>,
 <matplotlib.lines.Line2D at 0x15391a27430>,
 <matplotlib.lines.Line2D at 0x15391a27550>,
 <matplotlib.lines.Line2D at 0x15391a27670>,
 <matplotlib.lines.Line2D at 0x15391a27790>,
 <matplotlib.lines.Line2D at 0x15391a278b0>,
 <matplotlib.lines.Line2D at 0x15391a279d0>,
 <matplotlib.lines.Line2D at 0x15391a27af0>,
 <matplotlib.lines.Line2D at 0x15391a27c10>,
 <matplotlib.lines.Line2D at 0x15391a27d30>,
 <matplotlib.lines.Line2D at 0x15391a27e50>,
 <matplotlib.lines.Line2D at 0x15391a27f70>,
 <matplotlib.lines.Line2D at 0x15391a210d0>,
 <matplotlib.lines.Line2D at 0x15391a211f0>,
 <matplotlib.lines.Line2D at 0x15391a21310>,
 <matplotlib.lines.Line2D at 0x15391a21430>,
 <matplotlib.lines.Line2D at 0x15391a21550>,
 <matplotlib.lines.Line2D at 0x15391a21670>,
 <matplotlib.lines.Line2D at 0x15391a21790>,
 <matplotlib.lines.Line2D at 0x15391a218b0>,
 <matplotlib.lines.Line2D at 0x15391a219d0>,
 <matplotlib.lines.Line2D at 0x15391a21af0>,
 <matplotlib.lines.Line2D at 0x15391a21c10>,
 <matplotlib.lines.Line2D at 0x15391a21d30>,
 <matplotlib.lines.Line2D at 0x15391a21e50>,
 <matplotlib.lines.Line2D at 0x15391a21f70>,
 <matplotlib.lines.Line2D at 0x15391a280d0>,
 <matplotlib.lines.Line2D at 0x15391a281f0>,
 <matplotlib.lines.Line2D at 0x15391a28310>,
 <matplotlib.lines.Line2D at 0x15391a28430>,
 <matplotlib.lines.Line2D at 0x15391a28550>,
 <matplotlib.lines.Line2D at 0x15391a28670>,
 <matplotlib.lines.Line2D at 0x15391a28790>,
 <matplotlib.lines.Line2D at 0x15391a288b0>,
 <matplotlib.lines.Line2D at 0x15391a289d0>,
 <matplotlib.lines.Line2D at 0x15391a28af0>,
 <matplotlib.lines.Line2D at 0x15391a28c10>,
 <matplotlib.lines.Line2D at 0x15391a28d30>,
 <matplotlib.lines.Line2D at 0x15391a28e50>,
 <matplotlib.lines.Line2D at 0x15391a28f70>,
 <matplotlib.lines.Line2D at 0x15391a3f0d0>,
 <matplotlib.lines.Line2D at 0x15391a3f1f0>,
 <matplotlib.lines.Line2D at 0x15391a3f310>,
 <matplotlib.lines.Line2D at 0x15391a3f430>,
 <matplotlib.lines.Line2D at 0x15391a3f550>,
 <matplotlib.lines.Line2D at 0x15391a3f670>,
 <matplotlib.lines.Line2D at 0x15391a3f790>,
 <matplotlib.lines.Line2D at 0x15391a3f8b0>,
 <matplotlib.lines.Line2D at 0x15391a3f9d0>,
 <matplotlib.lines.Line2D at 0x15391a3faf0>,
 <matplotlib.lines.Line2D at 0x15391a3fc10>,
 <matplotlib.lines.Line2D at 0x15391a3fd30>,
 <matplotlib.lines.Line2D at 0x15391a3fe50>,
 <matplotlib.lines.Line2D at 0x15391a3ff70>,
 <matplotlib.lines.Line2D at 0x15391a080d0>,
 <matplotlib.lines.Line2D at 0x15391a081f0>,
 <matplotlib.lines.Line2D at 0x15391a08310>,
 <matplotlib.lines.Line2D at 0x15391a08430>,
 <matplotlib.lines.Line2D at 0x15391a08550>,
 <matplotlib.lines.Line2D at 0x15391a08670>,
 <matplotlib.lines.Line2D at 0x15391a08790>,
 <matplotlib.lines.Line2D at 0x15391a088b0>,
 <matplotlib.lines.Line2D at 0x15391a089d0>,
 <matplotlib.lines.Line2D at 0x15391a08af0>,
 <matplotlib.lines.Line2D at 0x15391a08c10>,
 <matplotlib.lines.Line2D at 0x15391a08d30>,
 <matplotlib.lines.Line2D at 0x15391a08e50>,
 <matplotlib.lines.Line2D at 0x15391a08f70>,
 <matplotlib.lines.Line2D at 0x15391aff0d0>,
 <matplotlib.lines.Line2D at 0x15391aff1f0>,
 <matplotlib.lines.Line2D at 0x15391aff310>,
 <matplotlib.lines.Line2D at 0x15391aff430>,
 ...]
In [18]:
mean_median_df = df2.copy()
w = 1000

df2['mean'] = df2.iloc[:, w:2*w].mean(axis=1)
df2['median'] = df2.iloc[:, w:2*w].median(axis=1)
df2
Out[18]:
prob_0 prob_1 prob_2 prob_3 prob_4 prob_5 prob_6 prob_7 prob_8 prob_9 ... balance 992 balance 993 balance 994 balance 995 balance 996 balance 997 balance 998 balance 999 mean median
0 0 1 1 0 0 1 0 0 0 1 ... 100 100 100 100 100 100 100 100 100.00 100.0
1 0 0 1 0 0 1 0 0 0 0 ... 150 150 60 150 150 150 150 60 106.17 150.0
2 0 0 0 0 0 1 0 1 0 0 ... 200 200 110 200 110 200 110 20 112.43 110.0
3 1 0 0 1 0 0 1 1 0 1 ... 250 160 160 160 160 250 70 -20 118.06 160.0
4 0 1 1 1 0 1 0 0 0 1 ... 210 210 120 120 120 210 30 -60 121.62 120.0
5 0 1 1 0 0 1 0 1 0 0 ... 260 170 170 80 170 170 80 -10 124.91 170.0
6 1 0 1 0 1 0 0 1 0 1 ... 220 130 220 130 130 220 40 -50 129.46 130.0
7 1 1 0 0 1 1 0 1 1 1 ... 180 90 270 90 90 270 90 -90 134.37 180.0
8 1 0 1 0 0 1 1 1 1 0 ... 140 140 320 50 140 230 140 -130 141.62 140.0
9 1 1 0 1 1 1 1 0 0 0 ... 190 100 280 100 100 190 100 -80 149.32 190.0

10 rows × 2002 columns

In [19]:
df2['mean'].plot()
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
plt.show()
In [20]:
df2['median'].plot()
plt.xlabel('Time in gamble rounds')
plt.ylabel('Wealth')
plt.show()

These new results are more favorable to the gambler and as they actually get to leave the place with more money than before, whereas the previous models indicate that after a certain number of rounds, the money eventually leaves the gamblers pocket and enters the casino, therefore making it a loss filled deal and gamble.

In [ ]: